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