Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Decay Rates for Inverses of Band Matrices

Stephen Demko, William F. Moss and Philip W. Smith
Mathematics of Computation
Vol. 43, No. 168 (Oct., 1984), pp. 491-499
DOI: 10.2307/2008290
Stable URL: http://www.jstor.org/stable/2008290
Page Count: 9
  • Read Online (Free)
  • Download ($34.00)
  • Subscribe ($19.50)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Decay Rates for Inverses of Band Matrices
Preview not available

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 $AA^\ast$ 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.

Page Thumbnails

  • Thumbnail: Page 
491
    491
  • Thumbnail: Page 
492
    492
  • Thumbnail: Page 
493
    493
  • Thumbnail: Page 
494
    494
  • Thumbnail: Page 
495
    495
  • Thumbnail: Page 
496
    496
  • Thumbnail: Page 
497
    497
  • Thumbnail: Page 
498
    498
  • Thumbnail: Page 
499
    499