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An analysis of the composite step biconjugate gradient method (1993)

Bank, Randolph E. ; Chan, Tony F.

Springer

Numerische Mathematik 66 (1993), S. 295-319

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ISSN: 0945-3245

Keywords: 65N20 ; 65F10

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Summary The composite step biconjugate gradient method (CSBCG) is a simple modification of the standard biconjugate gradient algorithm (BCG) which smooths the sometimes erratic convergence of BCG by computing only a subset of the iterates. We show that 2×2 composite steps can cure breakdowns in the biconjugate gradient method caused by (near) singularity of principal submatrices of the tridiagonal matrix generated by the underlying Lanczos process. We also prove a “best approximation” result for the method. Some numerical illustrations showing the effect of roundoff error are given.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01385699

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