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 need an accessible version of this item please contact JSTOR User Support

Inner and Outer Iterations for the Chebyshev Algorithm

Eldar Giladi, Gene H. Golub and Joseph B. Keller
SIAM Journal on Numerical Analysis
Vol. 35, No. 1 (Feb., 1998), pp. 300-319
Stable URL: http://www.jstor.org/stable/2587104
Page Count: 20
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
Inner and Outer Iterations for the Chebyshev Algorithm
Preview not available

Abstract

We analyze the preconditioned Chebyshev iteration in which at each step the linear system involving the preconditioner is solved inexactly by an inner iteration. We allow the tolerance used in the inner iteration to decrease from one outer iteration to the next. When the tolerance converges to zero, the asymptotic convergence rate is the same as for the exact method. Motivated by this result, we seek the sequence of tolerance values that yields the lowest cost to achieve a specified accuracy. We find that among all sequences of slowly varying tolerances, a constant one is optimal. Numerical calculations that verify our results are presented. Asymptotic methods, such as the W.K.B. method for linear recurrence equations, are used with an estimate of the accuracy of the asymptotic result.

Page Thumbnails

  • Thumbnail: Page 
300
    300
  • Thumbnail: Page 
301
    301
  • Thumbnail: Page 
302
    302
  • Thumbnail: Page 
303
    303
  • Thumbnail: Page 
304
    304
  • Thumbnail: Page 
305
    305
  • Thumbnail: Page 
306
    306
  • Thumbnail: Page 
307
    307
  • Thumbnail: Page 
308
    308
  • Thumbnail: Page 
309
    309
  • Thumbnail: Page 
310
    310
  • Thumbnail: Page 
311
    311
  • Thumbnail: Page 
312
    312
  • Thumbnail: Page 
313
    313
  • Thumbnail: Page 
314
    314
  • Thumbnail: Page 
315
    315
  • Thumbnail: Page 
316
    316
  • Thumbnail: Page 
317
    317
  • Thumbnail: Page 
318
    318
  • Thumbnail: Page 
319
    319