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Effective condition number for numerical partial differential equations

✍ Scribed by Zi-Cai Li; Hung-Tsai Huang

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
158 KB
Volume
15
Category
Article
ISSN
1070-5325

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✦ Synopsis

Abstract

In this paper, the new computational formulas are derived for the effective condition number Cond_eff, and the new error bounds involved in both Cond and Cond_eff are developed. A theoretical analysis is provided to support some conclusions in Banoczi et al. (SIAM J. Sci. Comput. 1998; 20:203–227). For the linear algebraic equations solved by the Gaussian elimination or the QR factorization (QR), the direction of the right‐hand vector is insignificant for the solution errors, but such a conclusion is invalid for the finite difference method for Poisson's equation. The effective condition number is important to the numerical partial differential equations, because the discretization errors are dominant. Copyright Β© 2008 John Wiley & Sons, Ltd.

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