On The Condition of Some Problems in Matrix Compuation

In numerical analysis, the condition number associated with a problem is a measure of that problem's amenability to digital computation, that is, how numerically well-posed the problem is. A problem with a low condition number is said to be well-conditioned, while a problem with a high condition number is said to be ill-conditioned. Classical condition numbers are normwise: they measure the size of both input perturbations and output errors using some norms. To take into account the relative of each data component, and, in particular, a possible data sparseness, componentwise condition numbers have been increasingly considered. These are mostly of two kinds: mixed and componentwise. In this book, we give explicit expressions, computable from the data, for the mixed and componentwise condition numbers for some problems in matrix computation, such as Moore- Penrose inverse, structured and unstructured linear least squares problems, structured and unstructured eigenvalue problems and smoothed analysis of some normwise condition numbers.

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Dr. Huaian Diao obtained PhD degree from City University of Hong Kong in 2007 and now is an associate professor of Northeast Normal University in China. He has published 18 refereed journal papers. His research is mainly in numerical linear algebra, especially in perturbation theory, structured matrices and generalized inverse.