Article View: sci.math.num-analysis
Article #1140Re: Condition Number
From: Fred Walsteijn
Date: Mon, 11 Jan 1993 14:48
Date: Mon, 11 Jan 1993 14:48
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1417 bytes
In <1993Jan11.083253.9521@dutrun2.tudelft.nl> rcpshdb@dutrun2.tudelft.nl (Han de Bruijn) writes:
>The condition number of a matrix A is defined as the absolute value of
>its largest eigenvalue divided by its smallest eigenvalue. Right?
>I'm at loss how this is related to the loss of decimals when solving the
>equations system:
> A.x = b
>Can someone out there provide a simple argument?
A perturbation "db" in the right hand side (due to rounding errors for
example) results in a change "dx" of the solution vector.
They are related by:
|dx| / |x| <= cond(A) |db| / |b|
The proof I am looking at right now assumes that A is symmetric...
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Fred Walsteijn | Internet: walsteyn@fys.ruu.nl
Institute for Marine and Atmospheric Research | FAX: 31-30-543163
Utrecht University, The Netherlands | Phone: 31-30-533169
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Newsgroups: sci.math.num-analysis Path: arc1-ca.pugleaf.net!sparky!uunet!mcsun!sun4nl!ruuinf!ruunfs.fys.ruu.nl!walsteyn From: walsteyn@fys.ruu.nl (Fred Walsteijn) Subject: Re: Condition Number Message-ID: <1993Jan11.144801.12633@fys.ruu.nl> Organization: Physics Department, University of Utrecht, The Netherlands References: <1993Jan11.083253.9521@dutrun2.tudelft.nl> Date: Mon, 11 Jan 1993 14:48:01 GMT Lines: 23