@MISC{_parallelcomputation, author = {}, title = {Parallel Computation of Pseudospectra using TransferFunctions on a MATLAB-MPI Cluster Platform}, year = {} }

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Abstract

Abstract. One of the most computationally expensive problems in numericallinear algebra is the computation of the ffl-pseudospectrum of matrices, that is, thelocus of eigenvalues of all matrices of the form A + E, where kEk ^ ffl. Severalresearch efforts have been attempting to make the problem tractable by means of better algorithms and utilization of all possible computational resources. Onecommon goal is to bring to users the power to extract pseudospectrum information from their applications, on the computational environments they generallyuse, at a cost that is sufficiently low to render these computations routine. To this end, we investigate a scheme based on i) iterative methods for computing pseu-dospectra via approximations of the resolvent norm, with ii) a computationalplatform based on a cluster of PCs and iii) a programming environment basedon MATLAB enhanced with MPI functionality and show that it can achieve high performance for problems of significant size. 1 Introduction and motivation Let A 2 C n\Theta n have singular value decomposition (SVD) A = U \Sigma V \Lambda, and let \Lambda (A) bethe set of eigenvalues of A. The ffl\Gamma pseudospectrum \Lambda ffl(A) (pseudospectrum for short)of a matrix is the locus of eigenvalues of