Eigenvalues and Pseudospectra of Rectangular Matrices
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چکیده
منابع مشابه
Pseudospectra of rectangular matrices
Pseudospectra of rectangular matrices vary continuously with the matrix entries, a feature that eigenvalues of these matrices do not have. Some properties of eigenvalues and pseudospectra of rectangular matrices are explored, and an efficient algorithm for the computation of pseudospectra is proposed. Applications are given in (square) eigenvalue computation (Lanczos iteration), square pseudosp...
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The concept of pseudospectra was introduced by Trefethen during the 1990s and became a popular tool to explain the behavior of non-normal matrices. It is well known that the zeros of a polynomial are equal to the eigenvalues of the associated companion matrix. It is feasible to do the sensitivity analysis of the zeros of polynomials by the tool of pseudospectra of companion matrices. Thus, the ...
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The pseudospectra of banded finite dimensional Toeplitz matrices rapidly converge to the pseudospectra of the corresponding infinite dimensional operator. This exponential convergence makes a compelling case for analyzing pseudospectra of such Toeplitz matrices—not just eigenvalues. What if the matrix is dense and its symbol has a jump discontinuity? The pseudospectra of the finite matrices sti...
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In this note, we discuss new techniques for analyzing the pseudospectra of matrices and propose a numerical method for computing the spectral projector associated with a group of eigenvalues enclosed by a polygonal curve. Numerital tests are reported.
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Definitions and characterizations of pseudospectra are given for rectangular matrix polynomials expressed in homogeneous form: P(α, β) = αAd + αd−1βAd−1 + · · · + βA0. It is shown that problems with infinite (pseudo)eigenvalues are elegantly treated in this framework. For such problems stereographic projection onto the Riemann sphere is shown to provide a convenient way to visualize pseudospect...
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