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Mathematics of Computation

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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 $ {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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DOI: https://doi.org/10.1090/S0025-5718-1984-0758197-9
Article copyright: © Copyright 1984 American Mathematical Society