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Please use this identifier to cite or link to this item: http://hdl.handle.net/1813/5573
Title: The Chebyshev Polynomials of a Matrix
Authors: Toh, Kim-Chuan
Trefethen, Lloyd N.
Keywords: theory center
Issue Date: May-1996
Publisher: Cornell University
Citation: http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.tc/96-240
Abstract: A Chebyshev polynomial of a square matrix A is a monic polynomial of specified degree that minimizes ||p(A)||(sub2). The study of such polynomials is motivated by the analysis of Krylov subspace iterations in numerical linear algebra. An algorithm is presented for computing these polynomials based on reduction to a semidefinite program which is then solved by a primal-dual interior point method. Examples of Chebyshev polynomials of matrices are presented, and it is noted that if A is far from normal, the lemniscates of these polynomials tend to approximate pseudospectra of A.
URI: http://hdl.handle.net/1813/5573
Appears in Collections:Cornell Theory Center Technical Reports

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