| The pseudospectra, first introduced by Prof. Trefethen of Oxford University in the1990s, havebecome a very useful tool to study and explain the behavior associated with non-normal matrices.Compared with spectra, the pseudospectra of matrices can provide more information for theexplanation of matrices behavior, but the calculation of pseudospectra of matrices is difficult andexpensive.Based on a comprehensive overview of the development and research of pseudospectra ofmatrices, the paper studies the definitions and computational methods of pseudospectra of Toeplitzmatrices. Firstly, based on the QR decomposition of Toeplitz matrices, a revised definition andcorresponding computational method are proposed. Then the computation method of pseudospectrabased on the adaptive grid method of SVD decomposition is further popularized and the adaptive gridmethod of QR decomposition for pseudospectra of Toeplitz is proposed. Secondly, based on QRdecomposition of block Toeplitz matrices, a computational method for pseudospectra of blockToeplitz matrices is proposed. For each method proposed in this paper, MATLAB is used to draw theimage of pseudospectra, conduct numerical experiments and compare the results for the illustration ofthe efficiency of the methods and algorithms. |
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