Skip to main content


eCommons@Cornell >
Faculty of Computing and Information Science >
Center for Advance Computing >
Cornell Theory Center Technical Reports >

Please use this identifier to cite or link to this item:
Title: The Chebyshev Polynomials of a Matrix
Authors: Toh, Kim-Chuan
Trefethen, Lloyd N.
Keywords: theory center
Issue Date: May-1996
Publisher: Cornell University
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.
Appears in Collections:Cornell Theory Center Technical Reports

Files in This Item:

File Description SizeFormat
96-240.pdf323 BAdobe PDFView/Open
96-240.ps372.12 kBPostscriptView/Open

Refworks Export

Items in eCommons are protected by copyright, with all rights reserved, unless otherwise indicated.


© 2014 Cornell University Library Contact Us