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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Vydané v:	SIAM journal on matrix analysis and applications Ročník 32; číslo 1; s. 286 - 308
Hlavní autori:	Bientinesi, Paolo, van de Geijn, Robert A.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2011
Predmet:	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
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Abstract	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]
AbstractList	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. 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]
Author	van de Geijn, Robert A. Bientinesi, Paolo
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SubjectTerms	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
Title	Goal-Oriented and Modular Stability Analysis
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