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2002•Numerical Linear Algebra with ApplicationsRequires access

Simultaneous backward stability of Gauss and Gauss–Jordan elimination

Juan Manuel Peña

Open publisher page 4 citations

Abstract

Abstract It is well known that some pivoting strategies are backward stable for Gauss elimination but are not backward stable for Gauss–Jordan elimination (GJE) when these procedures are used to solve a linear system Ax=b. We analyse the simultaneous backward stability for Gauss and GJE of several pivoting strategies, including a pivoting strategy which we call double partial pivoting. Copyright © 2002 John Wiley & Sons, Ltd.

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What this paper is about

Abstract It is well known that some pivoting strategies are backward stable for Gauss elimination but are not backward stable for Gauss–Jordan elimination (GJE) when these procedures are used to solve a linear system Ax=b. We analyse the simultaneous backward stability for Gauss and GJE of several pivoting strategies, including a pivoting strategy which we call double partial pivoting. Copyright © 2002 John Wiley & Sons, Ltd.

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Available abstract

Abstract It is well known that some pivoting strategies are backward stable for Gauss elimination but are not backward stable for Gauss–Jordan elimination (GJE) when these procedures are used to solve a linear system Ax=b. We analyse the simultaneous backward stability for Gauss and GJE of several pivoting strategies, including a pivoting strategy which we call double partial pivoting. Copyright © 2002 John Wiley & Sons, Ltd.

Key concepts: Gauss, Gaussian elimination, Mathematics, Stability (learning theory), Applied mathematics, Computer science, Gaussian, Chemistry

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