Pseudospectra Gateway

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This page describes a wide range of pseudospectral literature, including works that pre-date the term "pseudospectra" or use a synonymous term. It includes papers that develop pseudospectral theory or apply the concept in a specific context, but does not attempt to collect work from the broad field of spectral perturbation theory for non-normal matrices and operators.

Entries are sorted alphabetically by author. Where available, links to Mathematical Reviews on MathSciNet are given. You will only be able to view these links if your computer/institution is authorized access to MathSciNet. Similarly, we have begun to add links to articles that have been published electronically; if your computer is not authorized access to the corresponding site, you may only be able to view the abstract. Since these links are external, we cannot guarantee that they remain accurate. Please let us know if you find a link that no longer works.

This bibliography is continues to grow. If you know of a relevant paper omitted below, please notify us. Please also contact us should you find that any links are out of date.

In many cases, the references below are cross-listed on the Applications page. If you are looking specifically for papers related to a certain application, you might find it easier to begin there.

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Recent Updates
(also included in the comprehensive list that follows)

[BL07]

L. Boulton and P. Lancaster
On the boundary of the pseudospectrum and its fault points
arXiv.org e-Print archive http://arxiv.org/abs/math.SP/0702218

[Hag07]

M. Hager
Bound on the number of eigenvalues near the boundary of the pseudospectrum
Proc. Amer. Math. Soc. 135 (3867-3873), 2007.
Link to article

[KS07]

D. Kachuma and I. J. Sobey
Linear Instability of asymmetric Poiseuille flows
Oxford University Computing Laboratory Numerical Analysis Technical Report 07/21, November 2007.
Link to report

[Pra07]

K. Pravda-Starov
On the pseudospectrum of elliptic quadratic differential operators
arXiv.org e-Print archive arxiv:0704.0324

[VB07]

J. Vanneste and J. G. Byatt-Smith
Fast scalar decay in a shear flow: modes and pseudomodes
J. Fluid Mech. 572 (2007) 219-229.
Link to article

C. M. Aiken, A. M. Moore, and J. H. Middleton
The nonnormality of coastal ocean flows around obstacles, and their response to stochastic forcing
J. Phys. Oceanog. 32 (2002) 2955-2974.
Link to article

R. Alam and S. Bora
Stability of eigenvalues and spectral decompositions under linear perturbation
Linear Algebra Appl. 364 (2003) 189-211.

R. Alam and S. Bora
On sensitivity of eigenvalue and eigendecompositions of matrices
Linear Algebra Appl. 396 (2005) 273--301.
Link to article

A. Aslanyan and E. B. Davies
Spectral instability for some Schrödinger operators
Numer. Math. 85 (2000), 535-552. MR 2001e:34156
Link to article

O. G. Avsyankin and N. K. Karapetyants
On the pseudospectra of multidimensional integral operators with homogeneous kernels of degree-n
Siberian Math. J. 44 (2003) 935-950.
Link to article

J. S. Baggett
Pseudospectra of an operator of Hille and Phillips
ETH Interdisciplinary Project Center for Supercomputing Research Report 94-15, August 1994.

C. Beattie
Galerkin eigenvector approximations
Math. Comp. 69 (2000), 1409-1434. MR 2001a:65131
Link to article

C. Beattie, M. Embree, and J. Rossi
Convergence of restarted Krylov subspaces to invariant subspaces
Oxford University Computing Laboratory Numerical Analysis Technical Report 01/21, November 2001.
Link to report

C. Beattie, M. Embree, and D. C. Sorensen
Convergence of polynomial restart Krylov methods for eigenvalue computation
Rice University, Computational and Applied Mathematics Report TR03-08.
Link to report

C. Bekas and E. Gallopoulos
Cobra: Parallel path following for computing the matrix pseudospectrum
Parallel Computing 27 (2001) 1879-1896.
Link to article

C. Bekas and E. Gallopoulos
Parallel computation of pseudospectra by fast descent
Parallel Computing 28 (2002) 223-242.
Link to article

C. Bekas, E. Kokiopoulou, and E. Gallopoulos
The design of a distributed MATLAB-based environment for computing pseudospectra
Future Generation Computer Systems 21 (2005) 930-941.
Link to article

C. Bekas, E. Kokiopoulou, E. Gallopoulos, and V. Simoncini
Parallel computation of pseudospectra using transfer functions on a MATLAB-MPI cluster platform
Lecture Notes in Computer Science 2474 (2002) 199-207.
Link to article

C. Bekas, E. Kokiopoulou, E. Gallopoulos, and I. Koutis
Towards the effective parallel computation of matrix pseudospectra
Proc. ACM International Conference on Supercomputing, Sorrento, Italy, June 2001, p. 260-269.
Link to article

E. S. Benilov, S. B. G. O'Brien, and I. A. Sazonov
A new type of instability: Explosive disturbances in a liquid film inside a rotating horizontal cylinder.
J. Fluid Mech. 497 (2003) 201-224.
Link to article

B. Bernhardsson, A. Rantzer, and L. Qiu
Real perturbation values and real quadratic forms in a complex vector space
Linear Algebra Appl. 270 (1998), 131-154. MR 99a:15010
Link to article

T. R. Bewley
Flow control: New challenges for a new renaissance
Prog. Aerospace Sci. 37 (2001) 21-58.

T. R. Bewley
Model-based flow control for distributed architectures
Chapter 13, CRC MEMS Handbook, 2002.

S. Bora
A Geometric Analysis of Spectral Stability of Matrices and Operators
Ph.D. thesis, Indian Institute of Technology, Guwahati, July 2001.

D. Borba, K. S. Riedel, W. Kerner, G. T. A. Huysmans, M. Ottaviani, and P. J. Schmid
The pseudospectrum of the resistive magnetohydrodynamics operator: Resolving the resistive Alfvén paradox
Phys. Plasmas 1 (1994) 3151-3160.

D. Borthwick and A. Uribe
On the pseudospectra of Berezin-Toeplitz operators
Methods Appl. Analysis 10 (2003) 31-66. Link to article

A. Böttcher
Pseudospectra and singular values of large convolution operators
J. Integral Equations Appl. 6 (1994), 267-301. MR 96a:47044

A. Böttcher
Infinite matrices and projection methods
Lectures on Operator Theory and Its Applications (Waterloo, ON, 1994), 1-72, Fields Inst. Monogr. 3, AMS, Providence, RI, 1996. MR 96m:47016

A. Böttcher
C^*-algebras in numerical analysis
Irish Math. Soc. Bulletin 45 (2000) 57-133.
Links to Article: [postscript] [PDF]

A. Böttcher, M. Embree, and L. N. Trefethen
Piecewise continuous Toeplitz matrices and operators: slow approach to infinity
Oxford University Computing Laboratory Numerical Analysis Technical Report 00/19, August 2000.

A. Böttcher and S. M. Grudsky
Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis
Birkhäuser, Basel, 2000. MR 2001g:47043

A. Böttcher, S. M. Grudsky, and B. Silbermann
Norms of inverses, spectra, and pseudospectra of large truncated Wiener-Hopf operators and Toeplitz matrices
New York J. Math. 3 (1997) 1-31 (electronic). MR 98d:47057

A. Böttcher and B. Silbermann
Introduction to Large Truncated Toeplitz Matrices
Springer-Verlag, New York, 1999. MR 1 724 795

A. Böttcher and H. Wolf
Spectral approximation for Segal-Bargmann space Toeplitz operators
Linear Operators (Warsaw 1994), 25-48, Banach Center Publ. 38, Polish Acad. Sci., Warsaw, 1997. MR 98d:47055

L. S. Boulton
Non-self-adjoint harmonic oscillator, compact semigroups, and pseudospectra
arXiv.org e-Print archive math.SP/9909179.

L. Boulton and P. Lancaster
On the boundary of the pseudospectrum and its fault points
arXiv.org e-Print archive http://arxiv.org/abs/math.SP/0702218

L. Boulton, P. Lancaster, and P. Psarrakos
On pseudospectra of matrix polynomials and their boundaries
arXiv.org e-Print archive math.SP/0604229.

G. Boutry, M. Elad, G. H. Golub, and P. Milanfar
The generalized eigenvalue problem for nonsquare pencils using a minimal perturbation approach
SIAM J. Matrix Anal. Appl. 27 (2005) 582-601.
Link to article

T. Braconnier
Complete iterative method for computing pseudospectra
CERFACS Technical Report TR/PA/97/13, May 1997.
Link to report (gzipped postscript)

T. Braconnier and N. J. Higham
Computing the field of values and pseudospectra using the Lanczos method with continuation
BIT 36 (1996), 422-440. MR 97d:65015

T. Braconnier, R. A. McCoy, and V. Toumazou
Using the field of values for pseudospectra generation
CERFACS Technical Report TR/PA/97/28, September 1997.
Link to report (gzipped postscript)

B. M. Brown and M. Marletta
Spectral inclusion and spectral exactness for singular non-self-adjoint Sturm--Liouville problems
Proc. Roy. Soc. Lond. A 457 (2001) 117--139. Link to article

M. Brühl
A curve tracing algorithm for computing the pseudospectrum
BIT 36 (1996), 441-454. MR 97d:65016

H. Bulgak
Pseudoeigenvalues, spectral portrait of a matrix and their connections with different criteria of stability
In Error Control and Adaptivity in Scientific Computing, pp. 95-124, H. Bulgak and C. Zenger, eds., Kluwer, Dordrecht, 1999. MR 2001b:15010

H. Bulgak and D. Eminov
Computer dialogue system MVC
Selçuk J. Appl. Math 2 (2001) 17-38. Link to article

J. V. Burke, A. S. Lewis, and M. L. Overton
Robust stability and a criss-cross algorithm for pseudospectra
IMA J. Num. Anal. 23 (2003) 359-375. Link to article

J. V. Burke, A. S. Lewis, and M. L. Overton
Optimization and pseudospectra, with applications to robust stability
SIAM J. Matrix Anal. Appl. 25 (2004) 80-104. Link to article

J. V. Burke, A. S. Lewis, and M. L. Overton
Pseudospectral components and the distance to uncontrollability
SIAM J. Matrix Anal. Appl. 26 (2004) 350-361. Link to article

J. V. Burke, A. S. Lewis, and M. L. Overton
Optimization over pseudospectra
Preprint, 15 February 2002. Link to preprint (postscript)

J.-F. Carpraux, J. Erhel, and M. Sadkane
Spectral portrait for non-Hermitian large sparse matrices
Computing 53 (1994), 301-310. MR 97d:65016

F. Chaitin-Chatelin
Is nonnormality a serious computational difficulty in practice?
In R. F. Boisvert, ed., Quality of Numerical Software: Assessment and Enhancement, 300-314, Chapman and Hall, London, 1997.

F. Chaitin-Chatelin and V. Frayssé
Lectures on Finite Precision Computations
SIAM, Philadelphia, 1996. MR 97b:65059

F. Chaitin-Chatelin and S. Gratton
Convergence in finite precision of successive iteration methods under high nonnormality.
BIT 36 (1996), 455-469. MR 97h:65035

F. Chaitin-Chatelin and A. Harrabi
About definitions of pseudospectra of closed operators in Banach spaces
CERFACS Technical Report TR/PA/98/08, 1998.
Link to report (gzipped postscript)

F. Chaitin-Chatelin, V. Toumazou, and E. Traviesas
Accuracy assessment for eigencomputations: Variety of backward errors and pseudospectra
Linear Algebra Appl. 309 (2000), 73-83. MR 2001c:65041
Link to article

F. Chaitin-Chatelin and E. Traviesas
Homotopic perturbation: Unfolding the field of singularities of a matrix by a complex parameter: a global geometric approach
CERFACS Technical Report TR/PA/01/84, 2001.
Link to report (gzipped postscript)

S. Champier and L. Grammont
Note on the norm involved in the definition of the epsilon-spectrum
Applied Math. Lett. 14 (2001) 393-397.

T. Christiansen and M. Zworski
Pseudospectra in automorphic scattering
Preprint, Link to Preprint (postscript)

C. Cossu and J. M. Chomaz
Global measures of local convective instabilities
Phys. Rev. Lett. 78 (1997) 4387-4390.

J. D. Crawford
Pseudospectra of the linearized Vlasov equation
Bull. Am. Phys. Soc. 41 (1996) 1606 (abstract only).

J. K. Cullum and A. E. Ruehli
Pseudospectra analysis, nonlinear eigenvalue problems, and studying linear systems with delays
BIT 41 (2001) 265--281.

G. Dar, M. K. Verma, and V. Eswaran
Energy transfer in two-dimensional magnetohydrodynamic turbulence: formalism and numerical results
Physica D 157 (2001) 207-225.

J. M. Davis and S. M. Troian
Influence of boundary slip on the optimal excitations in thermocapillary driven spreading
Phys. Rev. E 70 (2004) 046309 (11 pages).
Link to article

D. L. Darmofal and P. J. Schmid
The importance of eigenvectors for local preconditioners of the Euler equations
J. Comp. Phys. 127 (1996), 346-362. MR 97d:76028

E. B. Davies
Pseudo-spectra, the harmonic oscillator and complex resonances
Proc. Roy. Soc. Lond. Ser. A 455 (1999), 585-599. MR 2000d:34183

E. B. Davies
Semi-classical states for non-self-adjoint Schrödinger operators
Commun. Math. Phys. 200 (1999), 35-41. MR 99m:34197

E. B. Davies
Pseudospectra of differential operators
J. Operator Theory 43 (2000), 243-262. MR 2001b:47034

E. B. Davies
Wild spectral behaviour of anharmonic oscillators
Bull. London Math. Soc. 32 (2000), 432-438.

E. B. Davies
Non-self-adjoint differential operators
Bull. London Math. Soc. 34 (2002) 513-532.

E. B. Davies
Semigroup growth bounds
arXiv.org e-Print archive math.SP/0302144

E. B. Davies
Approximating semigroups by using pseudospectra
arXiv.org e-Print archive math.SP/0303235

J. M. Davis and S. M. Troian
On a generalized approach to the linear stability of spatially nonuniform thin film flows
Phys. Fluids 15 (2003) 1344-1347.

J. P. Dedieu, M.-H Kim, M. Shub and F. Tisseur
Implicit gamma theorems (I): pseudoroots and pseudospectra
Manchester Centre for Computational Mathematics Numerical Analysis Report 394, November 2001.
FTP Link to report (gzipped postscript)

L. de Luca, M. Costa, and C. Caramiello
Energy growth of initial perturbations in two-dimensional gravitational jets
Phys. Fluids 14 (2002) 289-299.
Link to article

J. W. Demmel
A counterexample for two conjectures about stability
IEEE Trans. Automat. Control AC-32 (1987), 340-342.

J. W. Demmel
The geometry of ill-conditioning
J. Complexity 3 (1987), 201-229. MR 88h:65091

N. Dencker, J. Sjöstrand, and M. Zworski
Pseudospectra of semiclassical (pseudo-) differential operators
Comm. Pure Appl. Math. 57 (2004) 384--415.
Link to article

J. L. M. van Dorsselaer
Pseudospectra for matrix pencils and stability of equilibria
BIT 37 (1997), 833-845. MR 98m:65099

J. L. M. van Dorsselaer
Several concepts to investigate strongly nonnormal eigenvalue problems
SIAM J. Sci. Comput. 24 (2003), 1031--1053.

J. L. M. van Dorsselaer, J. F. B. M. Kraaijevanger, and M. N. Spijker
Linear stability analysis in the numerical solution of initial value problems
In Acta Numerica 1993, p. 199-237, Cambridge University Press, Cambridge, 1993. MR 94e:65051

T. A. Driscoll and L. N. Trefethen
Pseudospectra for the wave equation with an absorbing boundary
J. Comput. Appl. Math. 69 (1996), 125-142. MR 97e:65056

K. Du and Y. Wei
Structured pseudospectra and structured sensitivity of eigenvalues
J. Comp. Appl. Math. 197 (2006) 502-519. Link to article

A. Edelman and N. R. Rao
Random matrix theory
In Acta Numerica 2005, p. 233-297, Cambridge University Press, Cambridge, 2005. Link to article

M. Embree
How descriptive are GMRES convergence bounds?
Oxford University Computing Laboratory Numerical Analysis Technical Report 99/08, June 1999.

M. Embree and L. N. Trefethen
Generalizing eigenvalue theorems to pseudospectra theorems
SIAM J. Sci. Comp. 23 (2001), 583-590. Link to article

J. P. Flaherty, C. E. Seyler, and L. N. Trefethen
Large-amplitude transient growth in the linear evolution of equatorial spread F with a sheared zonal flow
J. Geophys. Res. 104 (1999), 6843-6857.

V. Frayssé, L. Giraud, and V. Toumazou
Parallel computation of spectral portraits on the Meiko CS2
In H. Liddell, A. Colbrook, B. Hertzberger, and P. Sloot, eds., High-Performance Computing and Networking, 312-318
Berlin: Springer-Verlag, 1996.

V. Frayssé, M. Gueury, F. Nicoud, and V. Toumazou
Spectral portraits for matrix pencils
CERFACS Technical Report TR/PA/96/19, August 1996.
Link to report (gzipped postscript)

M. I. Friswell and A. R. Champneys
Defective systems and pseudospectra
Materials Science Forum 440-441 (2003) 287-294.
Link to abstract

D. R. Fuhrman, H. B. Bingham, P. A. Madsen, and P. G. Thomsen
Linear and non-linear stability analysis for finite difference discretizations of high-order Boussinesq equations
Int. J. Numer. Methods Fluids 45 (2004) 751-773.
Link to article

E. Gallestey
Computing the spectral value sets using the subharmonicity of the norm of rational matrices
BIT 38 (1998), 22-33. MR 99b:65045

E. Gallestey, D. Hinrichsen, and A. J. Pritchard
Spectral value sets of infinite dimensional systems
In V. D. Blondel, D. D. Sontag, M. Vidyasagar, and J. C. Willems, eds., Open Problems in Mathematical Systems and Control Theory, 234-266.
Springer-Verlag, London, 1999.

E. Gallestey, D. Hinrichsen, and A. J. Pritchard
Spectral value sets of closed linear operators
Proc. Roy. Soc. Lond. Ser. A 456 (2000), 1397-1418.

S. K. Godunov
Modern Aspects of Linear Algebra
Translations of Mathematical Monographs volume 175, AMS, Providence, R.I., 1998.

S. K. Godunov, O. P. Kirilyuk, and V. I. Kostin
Spectral Portraits of Matrices
Preprint~3, Inst. of Math., Siberian Branch of USSR Acad. Sci., 1990. [Russian]

S. K. Godunov and M. Sadkane
Computation of pseudospectra via spectral projectors
Linear Algebra Appl. 279 (1998), 163-175. MR 99i:65046
Link to article

J. M. González de Durana and J.-M. Gracia
Nearest derogatory matrix when varying into a submatrix
Manuscript, July 2000.
Link to manuscript

J.-M. Gracia
Nearest submatrix that increases the geometric multiplicity
Manuscript, September 2000.

J.-M. Gracia and I. de Hoyos
Nearest pair with more nonconstant invariant factors and pseudospectrum
Linear Algebra Appl. 298 (1999) 143-158.
Link to article

S. Graillat
A note on structured pseudospectra
J. Comp. Appl. Math. 191 (2006) 68-76.
Link to article

L. Grammont and A. Largillier
On epsilon-spectra and stability radii
J. Comp. Appl. Math 147 (2002) 453-469.
Link to article

K. Green, A. R. Champneys, and M. I. Friswell
Analysis of the transient response of an automatic dynamic balancer for eccentric rotors
Int. J. Mech. Sciences 48 (2006) 274-293
Link to article

K. Green and T. Wagenknecht
Pseudospectra of delay differential equations
Bristol Centre for Applied Nonlinear Mathematics preprint 2004.27, 2004
Link to report

A. Greenbaum
Generalizations of the the field of values useful in the study of polynomial functions of a matrix
Linear Algebra Appl. 347 (2002) 233-249.

A. Greenbaum and L. N. Trefethen
Do the pseudospectra of a matrix determine its behavior?
Cornell University Department of Computer Science Technical Report 93-1371, August 1993.

R. Hagen, S. Roch, and B. Silbermann
C^*-Algebras and Numerical Analysis
Marcl Dekker, New York, 2000.

M. Hager
Instabilité spectrale semiclassique d'opérateurs non-autoadjoints
Ph.D. Thesis, École Polytechnique, June 2005

M. Hager
Bound on the number of eigenvalues near the boundary of the pseudospectrum
Link to article

A. Harrabi
Pseudospectre d'une suite d'opérateurs bornés
RAIRO Modél. Math. Anal. Numér. 32 (1998) 671-680. MR 99i:47005

A. Harrabi
Défaut de Normalité
CERFACS Technical Report TR/PA/98/36, 1998.
Link to report (gzipped postscript)

A. Harrabi
On the approximation of pseudospectra of nonnormal operators by discretization, Part I: the first deriviative operator
CERFACS Technical Report TR/PA/98/37, 1998.
Link to report (gzipped postscript)

A. Harrabi
On the approximation of pseudospectra of nonnormal operators by discretization, Part II: the convection-diffusion operator
CERFACS Technical Report TR/PA/98/38, 1998.
Link to report (gzipped postscript)

J. A. Hernández
High-order finite volume schemes for the advection-diffusion equation
Int. J. Num. Methods Eng. 53 (2002) 1211-1234. Link to article

V. Heuveline, B. Philippe, and M. Sadkane
Parallel computation of spectral portrait of large matrices by Davidson type methods
Numer. Algorithms 16 (1997), 55-75. MR 99i:65046

D. J. Higham and B. Owren
Nonnormality effects in a discretised nonlinear reaction-convection-diffusion equation
J. Comput. Phys. 124 (1996), 309-323. MR 97a:76094

D. J. Higham and L. N. Trefethen
Stiffness of ODEs
BIT 33 (1993), 285-303. MR 96a:65117

N. J. Higham
Accuracy and Stability of Numerical Algorithms, 2nd ed.
SIAM, Philadelphia, 2002.

N. J. Higham and P. A. Knight
Matrix powers in finite precision arithmetic
SIAM J. Matrix Anal. Appl. 16 (1995) 343-358. MR 96a:65080

N. J. Higham and F. Tisseur
A block algorithm for matrix 1-norm estimation, with an application to the 1-norm pseudospectra
SIAM J. Matrix Anal. Appl. 21 (2000) 1185-1201. MR 2001d:65051
Link to article

N. J. Higham and F. Tisseur
More on pseudospectra for polynomial eigenvalue problems and applications in control theory
Linear Algebra Appl. 351-352 (2002) 435-453.
FTP Link to Technical Report (gzipped postscript)

D. Hinrichsen and B. Kelb
Spectral value sets: a graphical tool for robustness analysis
Systems Control Lett. 21 (1993), 127-136. MR 94e:93038

D. Hinrichsen and A. J. Pritchard
On spectral variations under bounded real matrix perturbations
Numer. Math. 60 (1992), 509-524. MR 93a:65051

D. Hinrichsen and A. J. Pritchard
Stability of uncertain systems
Systems and Networks: Mathematical Theory and Applications, Vol. 1 (Regensburg, 1993), Math. Res. 77, Akademie-Verlag, Berlin, 1994. MR 95e:93059

D. Hinrichsen and A. J. Pritchard
On the transient behaviour of stable linear systems
Proceedings of the Fourteenth International Symposium of Mathematical Theory of Networks and Systems, Perpignan, France, 2000.

D. Hinrichsen and A. J. Pritchard
Mathematical Systems Theory I
Springer-Verlag, Berlin, 2005.
Link to website at Springer

M. Hitrik
Boundary spectral behavior for semiclassical operators in dimension one
Intern. Math. Res. Notices 2004:64 (2004) 3417-3438
Link to article

M. Hochbruck and C. Lubich
On Krylov subspace approximations to the matrix exponential operator
SIAM J. Numer. Anal. 34 (1997), 1911-1925. MR 97m:65085

M. E. Hochstenbach and B. Plestenjak
Backward error, condition numbers, and pseudospectra for the multiparameter eigenvalue problem Linear Algebra Appl. 375 (2003) 63--81
Link to article

H. Hristova, S. Roch, P. J. Schmid, L. S. Tuckerman
Transient growth in exactly counter-rotating Couette-Taylor flow
Theoret. Comput. Fluid Dynamics 16 (2002) 43-48.

H. Hristova, S. Roch, P. J. Schmid, L. S. Tuckerman
Transient growth in Taylor-Couette flow
Phys. Fluids 14 (2002) 3475-3484.

Z. Jackiewicz, B. Owren, and B. Welfert
Pseudospectra of waveform relaxation operators
Comput. Math. Appl. 36 (1998), 67-85. MR 99g:65086

Z. Jackiewicz and R. A. Renaut
A note on stability of pseudospectral methods for wave propagation
J. Comp. Appl. Math. 143 (2002) 127-139.

Y.-L. Jiang, R. M. M. Chen and O. Wing
Wavform relaxation operator and its spectra in circuit simulation under periodic excitation
IEEE International Symposium on Circuits and Systems, 2002: ISCAS 2002.
Link to article

Y.-L. Jiang and O. Wing
A note on the spectra and pseudospectra of waveform relaxation operators for linear differential-algebraic equations
SIAM J. Numer. Anal. 38 (2000), 186-201. MR 2001h:65089
Link to article

G. F. Jónsson and L. N. Trefethen
A numerical analyst looks at the "cutoff phenomenon" in card shuffling and other Markov chains
In D. F. Griffiths, D. J. Higham and G. A. Watson, eds., Numerical Analysis 1997 (Dundee, 1997), 150-178.
Longman Sci. Tech., Harlow, Essex, UK, 1998. MR 99i:65155

D. Kachuma and I. J. Sobey
Linear Instability of asymmetric Poiseuille flows
Oxford University Computing Laboratory Numerical Analysis Technical Report 07/21, November 2007.
Link to report

N. K. Karapetiants and S. G. Samko
Multi-dimensional integral operators with homogeneous kernels
Fract. Calc. Appl. Anal. 2 (1999), 67-96. MR 2000a:47102

V. Karlin
Cellular flames may exhibit a non-modal transient instability
Proc. Combust. Inst. 29 (2002) 1537-1542.

V. Karlin
Cellular flames may exhibit a non-modal transient instability
Math. Models Methods Appl. Sci. 14 (2004) 1191-1210.

M. Karow
Geometry of Spectral Value Sets
Ph.D. Thesis, Universität Bremen, 2003.

L. Kim and J. Moehlis
Transient growth for streak-streamwise vortex interactions
Phys. Let. A. 358 (2006) 431-437.
Link to article

V. I. Kostin
On definition of matrices' spectrum
In M. Durand and F. El Dabaghi, eds., High Performance Computing II, 407-414, North-Holland, Amsterdam, 1991.

V. I. Kostin and Sh. I. Razzakov
On convergence of the orthogonal power method for calculating a spectrum
Trudy Inst. Mat. 6 (Numerical methods in linear algebra) (1985), 55-84. MR 88d:65073

I. Koutis and E. Gallopoulos
Exclusion regions and fast estimation of pseudospectra
Preprint, 2002. Link to preprint (postscript)

P. Lancaster and P. Psarrakos
On the pseudospectra of matrix polynomials
SIAM J. Matrix Anal. Appl. 27 (2005), 115-129.
Link to article

H. J. Landau
On Szegö's eigenvalue distribution theory and non-Hermitian kernels
J. d'Analyse Math. 28 (1975), 335-357.

H. J. Landau
Loss in unstable resonators
J. Opt. Soc. Amer. 66 (1976), 525-529. MR 54 #11988

H. J. Landau
The notion of approximate eigenvalues applied to an integral equation of laser theory
Quart. Appl. Math. 35 (1977), 165-172. MR 56 #4433

P.-F. Lavallée, A. Malyshev, and M. Sadkane
Spectral portrait of matrices by block diagonalization
In Numerical Analysis and its Applications (Rousse, 1996), Lecture Notes in Comput. Sci. 1196, pp. 266-273, Springer, Berlin, 1997.

P.-F. Lavallée and M. Sadkane
Pseudospectra of linear matrix pencils by block diagonalization
Computing 60 (1998), 133-156. MR 99e:65062

P.-F. Lavallée and M. Sadkane
Computation of pseudospectra by spectral dichotomy methods in a parallel environment
Numer. Algorithms 33 (2003) 343-355.
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B.-C. Li and Z. Sun
Generalization of generalized eigenvalue theorems to pseudospectra theorems
J. Nanjing Univ. Sci. Tech. 29 (2005) 113-115.
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M. Liefvendahl
A Chebyshev tau spectral method for the calculation of eigenvalues and pseudospectra
Technical Report TRITA-NA-0125, Nada, KTH, 2001.
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R. A. Lippert and A. Edelman
The computation and sensitivity of double eigenvalues
In Advances in Computational Mathematics: Proceedings of the Guangzhou International Symposium, Z. Chen, Y. Li, C. A. Micchelli, and Y. Xu, eds, pp. 353---393, Dekker, New York, 1999. MR 2000e:65043

Y. Liu and D. Cai
Inhomogeneous eigenvalue problems
Tsinghua Sci. Technol. 3 (1998), 1260-1264. MR 99j:65059

G. Lohmann
Pseudospectrum of equatorial waves
Manuscxript, 2000. Link to abstract , postcript file

S. H. Lui
Computation of pseudospectra by continuation
SIAM J. Sci. Comput. 18 (1997), 565-573. MR 98j:65028

A. Lumsdaine and D. Wu
Spectra and pseudospectra of block Toeplitz matrices
Linear Algebra Appl. 272 (1997), 103-130. MR 99b:65048
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A. Lumsdaine and D. Wu
Spectra and pseudospectra of waveform relaxation operators
SIAM J. Sci. Comput. 18 (1997), 286-304. MR 97k:65092

A. N. Malyshev and M. Sadkane
Componentwise pseudospectrum of a matrix
Linear Algebra Appl. 378 (2004) 283--288.
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O. A. Marques and V. Toumazou
Spectral portrait computation by a Lanczos method
CERFACS Technical Report TR/PA/95/05, February 1995.
Link to report (gzipped postscript)

R. V. N. Melnik
Topological analysis of eigenvalues in engineering computations
Eng. Computations 17 (2000) 386-416.
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E. Mengi and M. L. Overton
Algorithms for the computation of the pseudospectral radius and the numerical radius of a matrix
IMA J. Num. Anal. 25 (2005) 648-669.
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Á. Meseguer and L. N. Trefethen
A spectral Petrov-Galerkin formulation for pipe flow, I: Linear stability and transient growth
Oxford University Computing Laboratory Numerical Analysis Technical Report 00/18, September 2000.
Link to report

Á. Meseguer and L. N. Trefethen
Linearized pipe flow to Reynolds number 10⁷
Oxford University Computing Laboratory Numerical Analysis Technical Report 02/09, May 2002.
Link to report

D. Mezher
A graphical tool for driving the parallel computation of pseudospectra
Proc. ACM International Conference on Supercomputing, Sorrento, Italy, June 2001, p. 270-276.
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D. Mezher and B. Philippe
PAT - a reliable path-following algorithm
Numerical Algorithms 29 (2002) 131-152. MR 2003b:65037

D. Mezher and B. Philippe
Parallel computation of pseudospectra of large sparse matrices
Parallel Computing 28 (2002) 199-221.
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N. M. Nachtigal, S. C. Reddy, and L. N. Trefethen
How fast are nonsymmetric matrix iterations?
SIAM J. Matrix Anal. Appl. 13 (1992) 778-795. MR 93a:65039

N. M. Nachtigal, L. Reichel, and L. N. Trefethen
A hybrid GMRES algorithm for nonsymmetric linear systems
SIAM J. Matrix Anal. Appl. 13 (1992), 796-825. MR 93a:65040

L. Nedelec
Perturbations of non self-adjoint Sturm-Liouville problems, with applications to harmonic oscillators
arXiv.org e-Print archive math.SP/0406491

O. Nevanlinna
Convergence of Iterations for Linear Equations
Birkhauser, Basel, 1993. MR 9rh:65055

P. J. Olsson and D. S. Henningson
Optimal disturbance growth in groundwater flow
Studies Applied Math. 94 (1995), 183-210. MR 96a:76049

R. Plato
Resolvent estimates for Abel integral operators and the regularization of associated first kind integral equations
J. Integral Equations Appl. 9 (1997), 253-278. MR 99i45005

K. Pravda-Starov
A general result about the pseudo-spectrum of Schrödinger operators
Proc. Roy. Soc. Lond. A 460 (2004) 471--477.
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K. Pravda-Starov
Etude du pseudo-spectre et des instabilités spectrales de certaines classes d'opérateurs pseudo-différentiels non auto-adjoints
Ph.D. Thesis, Université Rennes 1.
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K. Pravda-Starov
Pseudo-spectrum for a class of semi-classical operators
Manuscript.
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K. Pravda-Starov
A complete study of the pseudo-spectrum for the rotated harmonic oscillator
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K. Pravda-Starov
On the pseudospectrum of elliptic quadratic differential operators
arXiv.org e-Print archive arxiv:0704.0324

S. C. Reddy
Pseudospectra of Wiener-Hopf integral operators and constant-coefficient differential operators
J. Integral Equations Appl. 5 (1993), 369-403. MR 94m:47057

S. C. Reddy and D. S. Henningson
Energy growth in viscous channel flows
J. Fluid Mech. 252 (1993), 209-238. MR 94e:76032

S. C. Reddy, P. J. Schmid, and D. S. Henningson
Pseudospectra of the Orr-Sommerfeld operator
SIAM J. Appl. Math. 53 (1993), 15-47. MR 94g:76021

S. C. Reddy and L. N. Trefethen
Lax-stability of fully discrete spectral methods via stability regions and pseudo-eigenvalues
Comput. Methods Appl. Mech. Engrg. 80 (1990) 147-164. MR 91j:65102

S. C. Reddy and L. N. Trefethen
Stability of the method of lines
Numer. Math. 62 (1992), 235-267. MR 93d:65086

S. C. Reddy and L. N. Trefethen
Pseudospectra of the convection-diffusion operator
SIAM J. Appl. Math. 54 (1994), 1634-1649. MR 95k:47108

P. Redparth
The pseudospectral properties of non-self-adjoint Schrödinger operators in the semi-classical limit
arXiv.org e-Print archive math.SP/0007172

P. Redparth
Spectral properties of non-self-adjoint operators in the semi-classical regime
J. Differential Equations 177 (2001) 307-330.
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L. Reichel and L. N. Trefethen
Eigenvalues and pseudo-eigenvalues of Toeplitz matrices
Linear Algebra Appl. 162/164 (1992), 153-185. MR 92k:15028

R. Renaut
Stability of a Chebyshev pseudospectral solution of the wave equation with absorbing boundaries
J. Comput. Appl. Math. 87 (1997) 243-259. MR 99b:65123

K. S. Riedel
Generalized epsilon-pseudospectra
SIAM J. Numer. Anal. 31 (1994), 1219-1225. MR 96a:15007

M. Robbé and M. Sadkane
Discrete-time Lyapunov stability of large matrices
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S. Roch and B. Silbermann
C*-algebra techniques in numerical analysis
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S. Roch
Spectral approximation of Wiener-Hopf operators with almost periodic generating function
Numer. Funct. Anal. Optim. 21 (2000), 241-253. MR 2001k:65206

S. Roch
Pseudospectra of operator polynomials
Operator Theory Adv. Appl. 124 (2001), 545-558. MR 2002d:47020

A. Ruhe
The rational Krylov algorithm for large nonsymmetric eigenvalues - mapping the resolvent norms (pseudospectrum)
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S. Rump
Structured perturbations. I. Norwise distances
SIAM J. Matrix Anal. Appl. 25 (2003), 1-30.
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S. M. Rump
Eigenvalues, pseudospectrum and structured perturbationss
Linear Algebra Appl. 413 (2006), 567-593.
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P. J. Schmid
Linear stability theory and bypass transition in shear flows
Phys. Plasmas 7 (2000), 1788-1794.

P. J. Schmid and D. S. Henningson
Stability and Transition in Shear Flows
Springer-Verlag, New York, 2001.

Y. Shen, J. Zhao, and H. Fan
Properties and computations of matrix pseudospectra
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V. Simoncini
Ritz and pseudo-Ritz values using matrix polynomials
Linear Algebra Appl. 241-243 (1996), 272-801. MR 97e:65034

V. Simoncini
A matrix analysis of Arnoldi and Lanczos methods
Numer. Math. 81 (1998), 125-141. MR 99j:65061

V. Simoncini
Remarks on non-linear spectral perturbation
BIT 39 (1999), 350-365. MR 2000g:15006

V. Simoncini and E. Gallopoulos
Convergence properties of block GMRES and matrix polynomials
Lin. Alg. Appl. 247 (1996), 97-119. MR 97k:65094

V. Simoncini and E. Gallopoulos
Transfer functions and resolvent norm approximation of large matrices
Elec. Trans. Numer. Anal. 7 (1998), 190-201 (electronic). MR 99i:65039

J. Sjöstrand
Pseudospectrum for differential operators
Seminar notes, Equations aux Dérivées Partielles, Centre de Mathéatiques de l'Ecole Polytechnique, 2002-2003.
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D. C. Sorensen
Numerical methods for large eigenvalue problems
Acta Numerica 11 (2002), 519-584.

M. K. Tippett and D. Marchesin
Upper bounds for the solution of the discrete algebraic Lyapunov equation
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F. Tisseur and N. J. Higham
Structured pseudospectra for polynomial eigenvalue problems, with applications
SIAM J. Matrix Anal. Appl. 23 (2001), 187-208. Link to article

K.-C. Toh
Matrix Approximation Problems and Nonsymmetric Iterative Methods
Ph.D. thesis, Cornell University, 1996.

K.-C. Toh and L. N. Trefethen
Pseudozeros of polynomials and pseudospectra of companion matrices
Numer. Math. 68 (1994) 403-425. MR 95m:65085

K.-C. Toh and L. N. Trefethen
Calculation of pseudospectra by the Arnoldi iteration
SIAM J. Sci. Comput. 17 (1996), 1-15. MR 97i:65064

K.-C. Toh and L. N. Trefethen
The Chebyshev polynomials of a matrix
SIAM J. Matrix Anal. Appl. 20 (1999), 400-419. MR 99m:15028

K.-C. Toh and L. N. Trefethen
The Kreiss matrix theorem on a general complex domain
SIAM J. Matrix Anal. Appl. 21 (1999), 145-165. MR 2000h:65054

V. Toumazou and E. Traviesas
A note on the homotopic backward error and pseudospectra for the generalized eigenproblem Ax=lambda Bx
CERFACS Technical Report TR/PA/99/14, April 1999.
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A. E. Trefethen, L. N. Trefethen, and P. J. Schmid
Spectra and pseudospectra for pipe Poiseuille flow
Comput. Methods Appl. Mech. Engrg. 175 (1999), 413-420. MR 2000c:76069

L. N. Trefethen
Approximation theory and numerical linear algebra
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L. N. Trefethen
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L. N. Trefethen
Pseudospectra of linear operators
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L. N. Trefethen
Computation of pseudospectra
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L. N. Trefethen
Spectra and pseudospectra
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L. N. Trefethen
Spectral Methods in MATLAB
SIAM, Philadelphia, 2000.

L. N. Trefethen
Wave packet pseudomodes of variable coefficient differential operators
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L. N. Trefethen and S. J. Chapman
Wave packet pseudomodes of twisted Toeplitz matrices
Comm. Pure Appl. Math. 57 (2004) 1233-1264.
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L. N. Trefethen, M. Contedini, and M. Embree
Spectra, pseudospectra, and localization for random bidiagonal matrices
Comm. Pure Appl. Math. 54 (2001), 595-623.
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L. N. Trefethen and M. Embree
Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators
Princeton University Press, Princeton, NJ, 2005.
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L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll
Hydrodynamic stability without eigenvalues
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Fast scalar decay in a shear flow: modes and pseudomodes
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J. M. Varah
The computation of bounds for the invariant subspaces of a general matrix operator
Technical Report CS 66, Computer Science Department, Stanford University, May 1967.

J. M. Varah
On the separation of two matrices
SIAM J. Numer. Anal. 16 (1979), 216-222. MR 81h:65038

W. A. van der Veen, J. J. B. de Swart, and P. J. van der Houwen
Convergence aspects of step-parallel iteration of Runge-Kutta methods
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D. Viswanath and L. N. Trefethen
Matrix Behaviour, Unitary Reducibility, and Hadamard Products
Cornell University Department of Computer Science Technical Report 96-1596, July 1996.

T. Wagenknecht and J. Agarwal
Structured pseudospectra in structural engineering
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J. H. Wilkinson
Sensitivity of Eigenvalues II
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M. P. H. Wolff
On the approximation of operators and the convergence of the spectra of the approximants
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M. P. H. Wolff
Discrete approximation of unbounded operators and approximation of their spectra
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T. G. Wright
Algorithms and Software for Pseudospectra
DPhil Thesis, Oxford, 2002.

T. G. Wright and L. N. Trefethen
Large-scale computation of pseudospectra using ARPACK and Eigs
SIAM J. Sci. Comp. 23 (2001), 591-605.
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T. G. Wright and L. N. Trefethen
Pseudospectra of rectangular matrices
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J. Yamasaki and N. Hatano
A new algorithm of analyzing the metal-insulator transition of the Anderson model
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Y. Zhang, V. Dymnikov, and J. M. Wallace
Sensitivity test of POP system matrices - an application of spectral portrait of a nonsymmetric matrix
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M. Zworski
A remark on a paper of E. B. Davies
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M. Zworski
Numerical linear algebra and solvability of partial differential equations
Comm. Math. Phys. 229 (2002) 293-307. Link to article