Decay rates for inverses of band matrices

Authors:
Stephen Demko, William F. Moss and Philip W. Smith

Journal:
Math. Comp. **43** (1984), 491-499

MSC:
Primary 15A09; Secondary 15A60, 65F15

DOI:
https://doi.org/10.1090/S0025-5718-1984-0758197-9

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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DOI:
https://doi.org/10.1090/S0025-5718-1984-0758197-9

Article copyright:
© Copyright 1984
American Mathematical Society