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Gaussian Elimination and Numerical Instability

Robert D. Skeel

出版	Department of Computer Science, University of Illinois at Urbana-Champaign, 1977
URL	http://books.google.com.hk/books?id=nqKNKE1RNWoC&hl=&source=gbs_api

註釋

Roundoff error in the solution of linear algebraic systems is studied using a more realistic notion of what it means to perturb a problem, namely that each datum is subject to a relatively small change. The condition number is determined for this approach. A good computable error bound is given for the 'backward error'. The effect of scaling on the stability of Gaussian elimination is studied, and it is discovered that the proper way to scale a system is dependent on knowing the solution. Finally it is shown that Gaussian elimination can be stabilized by doing iterative improvement. (Author).