Paper Info
Title
Effective condition number for numerical partial differential equations
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 (C) 2008 John Wiley & Sons, Ltd.
Year
DOI
Venue
2008
10.1002/nla.584
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
Keywords
Field
DocType
condition number,effective condition number,stability analysis,numerical PDE,Poisson's equation
Differential equation,Discretization,Condition number,Mathematical analysis,Numerical partial differential equations,First-order partial differential equation,Finite difference method,Stiffness matrix,Numerical stability,Mathematics
Journal
Volume
Issue
ISSN
15
7
1070-5325
Citations 
PageRank 
References 
5
0.83
6
Authors
2
Name
Order
Citations
PageRank
Zi-Cai Li112518.79
Hung-Tsai Huang2184.99