๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

A computable error bound for matrix functionals

โœ Scribed by D. Calvetti; G.H. Golub; L. Reichel

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
243 KB
Volume
103
Category
Article
ISSN
0377-0427

No coin nor oath required. For personal study only.

โœฆ Synopsis

Many problems in applied mathematics require the evaluation of matrix functionals of the form F(A):= uTf(A)u, where A is a large symmetric matrix and u is a vector. Golub and collaborators have described how approximations of such functionals can be computed inexpensively by using the Lanczos algorithm. The present note shows that error bounds for these approximations can be computed essentially for free when bounds for derivatives of f on an interval containing the spectrum of A are available. (~) 1999 Elsevier Science B.V. All rights reserved.

๐Ÿ“œ SIMILAR VOLUMES

On error bounds for eigenvalues of a mat
On error bounds for eigenvalues of a matrix pencil
โœ Mario Ahues; Balmohan Limaye ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 564 KB

An error bound for approximate eigenvalues of a complex n-dimensional pencil (A, B) is given. From our theorem several well-known bounds follow as corollaries. Our result takes into account the general residual AX -BXW, where X ~ C n x m and W ~ C mxm with m ~< n.