On the Conditioning of the Nonsymmetric Eigenproblem: Theory and Software (Classic Reprint) - Softcover

Bai, Z.

Softcover

ISBN 10: 1334016755 ISBN 13: 9781334016752

Publisher: Forgotten Books, 2019

Synopsis

Excerpt from On the Conditioning of the Nonsymmetric Eigenproblem: Theory and Software

The condition number of a problem measures the sensitivity of the solution to small changes in the input. We call the problem ill-conditioned if its condition number is large, and ill-posed if its condition number is infinite. We may use condition numbers to bound errors in computed solutions of numerical problems.

We illustrate this with a simple example. It is well known that the condition number for solving a system of linear equations is ic(a) E A where [i II is any matrix operator norm (we will be more specific about norms later). Suppose that linear system Ar. B is solved via Gaussian elimination with partial pivoting, or some other stable scheme. Let f be the computed solution. Then one may bound the error by.

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Edition details

• Publisher: Forgotten Books
• Publication date: 2019
• Language: English
• ISBN 10: 1334016755
• ISBN 13: 9781334016752
• Binding: Paperback
• Number of pages: 43