On The Pseudospectra Of Structured Matrices

The pseudospectra was introduced by Prof Trefethen of Oxford University became a useful tool tostudy and explain the behavior of systems associated with non-normal matrices. Comparing withspectra, the pseudospectra of matrices can give more information than the spectra, but it is difficultand expensive to compute. In this paper, based on a comprehen-description on the research work ofpseudospectra of matrices, the definitions and computational methods of pseudospectra of strucuturematrices are studied. Firstly, the definition and computational method of Toeplitz matrices areproposed. And the adaptive grid method for conputing pseudospectra of Teoplitz is propsoed. Then,the definitions and computational methods of rectangular Toeplitz matrices are proposed. At last, thisidea are generalized to case of the block Toeplitz matrices (including general block Toeplitz matricesand triangle block Toeplitz matrices). For each method which we proposed in this paper, experimentswere done to illustrate the efficiency of the methods and algorithms.