The Concept of Stability in Numerical Mathematics


题目The Concept of Stability in Numerical Mathematics

报告人Prof. Dr. Rudolf Scherer KIT, Karlsruhe, Germany



摘要Stability is a concept that appears in various fields of numerical mathematics as well as in other parts of mathematics, and there is a common meaning for stability, roughly described by the fact that perturbations are not amplifying the result in a dangerous way. But mostly in each subfield stability is differently defined. Although the stability definition is inspired by numerical phenomena, it is also suited to purely analytical purposes. In numerical mathematics, we have to distinguish between finite algorithms, such as Gauss elimination method for solving a system of linear equations, and approximation algorithms where consistency, convergence and stability are important, such as fixpoint methods and discrete methods for differential equations. This lecture presents an overview to stability concepts in numerical mathematics.



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