Yuguang Huang, Date to be advised, 25pp In this report, we give some efficient algorithms for structured matrix computations. The matrices involved are tridiagonal matrix and skew-symmetric matrix. More specifically, we first investigate into the tridiagonal system solvers using linear recurrence and a two-way strategy. Based on that, an optimal tridiagonal matrix inversion algorithm is further derived. For the skew-symmetric system, we give an efficient iterative algorithm using the idea of conjugate gradient method. The parallel complexity issues are discussed using the Bulk Synchronous Parallel model.