Effective condition number for numerical partial differential equations
Zi‐Cai Li, Hung‐Tsai Huang · Numerical Linear Algebra with Applications · 2008
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 © 2008 John Wiley & Sons, Ltd.