Accession Number:

ADA604544

Title:

Analysis of the Finite Precision s-Step Biconjugate Gradient Method

Descriptive Note:

Technical rept.

Corporate Author:

CALIFORNIA UNIV BERKELEY DEPT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCES

Personal Author(s):

• Carson, Erin
• Demmel, James

Report Date:

2014-03-13

Pagination or Media Count:

19.0

Abstract:

We analyze the s-step biconjugate gradient algorithm in nite precision arithmetic and derive a bound for the residual norm in terms of a minimum polynomial of a perturbed matrix multiplied by an ampli cation factor. Our bound enables comparison of s-step and classical biconjugate gradient in terms of ampli cation factors. Our results show that for s-step biconjugate gradient the ampli cation factor depends heavily on the quality of s-step polynomial bases generated in each outer loop.

Descriptors:

• *ALGORITHMS
• *GRADIENTS
• ARITHMETIC
• LINEAR SYSTEMS
• LOOPS
• PERTURBATIONS
• POLYNOMIALS

Subject Categories:

• Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE