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Published in:
2021 | OriginalPaper | Chapter
10. Conditioning and Well-Posedness
Author : Tobias Weinzierl
Published in: Principles of Parallel Scientific Computing
Publisher: Springer International Publishing
Abstract
Hadamard’s definition of well-posedness makes us start to think if a particular problem is solvable on a computer at all. We introduce the terms well-conditioned and ill-conditioned, and finally define the condition number to quantify how sensitive an algorithm is to slight changes of its input. After a brief excursus what the condition number means for linear equation systems—it turns out to be a special case of our more generic definition—we discuss the interplay of the conditioning with forward stability and introduce backward stability as evaluation condition number.
