Scaling for Numerical Stability in Gaussian Elimination

Abstract

Roundoff error m the solution of hnear algebraic systems is stud,ed using a more reahstsc notion of what st means to perturb a problem, namely, that each datum is subject to a relatwely small change This is particularly appropriate for sparse linear systems The condition number :s determined for th:s approach The effect of scahng on the stabdlty of Gaussmn ellmmat,on is stud:ed, and st is d:scovered that the proper way to scale a system depends on the right-hand s:de However, ff only the norm of the error is of concern, then there is a good way to scale that does not depend on the right-hand side. © 1979, ACM. All rights reserved.