Matrix Computation and the Theory of Moments

Gene Golub
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Gene Golub: Stanford University, Computer Science Department

A chapter in Proceedings of the International Congress of Mathematicians, 1995, pp 1440-1448 from Springer

Abstract: Abstract We study methods to obtain bounds or approximations to uT f(A)v where A is a symmetric, positive definite matrix and f is a smooth function. These methods are based on the use of quadrature rules and the Lanczos algorithm. We give some theoretical results on the behavior of these methods based on results for orthogonal polynomials as well as analytical bounds and numerical experiments on a set of matrices for several functions f. We discuss the effect of rounding error in the quadrature calculation.

Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-9078-6_140

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DOI: 10.1007/978-3-0348-9078-6_140

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