## Decay rates for inverses of band matrices

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- by Stephen Demko, William F. Moss and Philip W. Smith PDF
- Math. Comp.
**43**(1984), 491-499 Request permission

## 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 ${A^{ - 1}}$ can be bounded in terms of the (essential) spectrum of $A{A^\ast }$ 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

- © Copyright 1984 American Mathematical Society
- 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