Approximation algorithms for MAX-3-CUT and other problems via complex semidefinite programming
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximation algorithms for MAX-3-CUT and other problems via complex semidefinite programming
Journal of Computer and System Sciences - STOC 2001
On Chebyshev Polynomials of Matrices
SIAM Journal on Matrix Analysis and Applications
An Error Analysis for Rational Galerkin Projection Applied to the Sylvester Equation
SIAM Journal on Numerical Analysis
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A Chebyshev polynomial of a square matrix A is a monic polynomial p of specified degree that minimizes |p (A)|2. 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.