Goal-Oriented and Modular Stability Analysis

We introduce a methodology for obtaining inventories of error results for families of numerical dense linear algebra algorithms. The approach for deriving the analyses is goal-oriented, systematic, and layered. The presentation places the analysis side-by-side with the algorithm so that it is obviou...

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Bibliographic Details
Published in:SIAM journal on matrix analysis and applications Vol. 32; no. 1; pp. 286 - 308
Main Authors: Bientinesi, Paolo, van de Geijn, Robert A.
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2011
Subjects:
Algebra
Algorithms
Blocking
Error analysis
Errors
Exact sciences and technology
Factorization
Inventories
Linear algebra
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematics
Mean square errors
Modular
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
Several complex variables and analytic spaces
Stockpiling
Studies
modular
Error estimation
LU factorization
Methodology
Support
automatic stability analysis
Numerical linear algebra
stability analysis
Error bound
Algorithm
Layer
Numerical analysis
Linear algebra
Automatic analysis
Algorithm analysis
ISSN:0895-4798, 1095-7162
Online Access:Get full text
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Summary:We introduce a methodology for obtaining inventories of error results for families of numerical dense linear algebra algorithms. The approach for deriving the analyses is goal-oriented, systematic, and layered. The presentation places the analysis side-by-side with the algorithm so that it is obvious where roundoff error is introduced. The approach supports the analysis of more complex algorithms, such as the blocked LU factorization. For this operation we derive a tighter error bound than has been previously reported in the literature. [PUBLICATION ABSTRACT]
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ISSN:0895-4798
1095-7162
DOI:10.1137/080741057