Decay rates for inverses of band matrices
Authors:
Stephen Demko, William F. Moss and Philip W. Smith
Journal:
Math. Comp. 43 (1984), 491499
MSC:
Primary 15A09; Secondary 15A60, 65F15
MathSciNet review:
758197
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Abstract: Spectral theory and classical approximation theory are used to give a new proof of the exponential decay of the entries of the inverse of band matrices. The rate of decay of can be bounded in terms of the (essential) spectrum of for general A and in terms of the (essential) spectrum of A for positive definite A. In the positive definite case the bound can be attained. These results are used to establish the exponential decay for a class of generalized eigenvalue problems and to establish exponential decay for certain sparse but nonbanded matrices. We also establish decay rates for certain generalized inverses.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198407581979
PII:
S 00255718(1984)07581979
Article copyright:
© Copyright 1984
American Mathematical Society
