Pub. Date:
VDM Verlag
On The Condition Of Some Problems In Matrix Compuation

On The Condition Of Some Problems In Matrix Compuation

by Huaian Diao


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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.

Product Details

ISBN-13: 9783639111095
Publisher: VDM Verlag
Publication date: 09/06/2009
Pages: 92
Product dimensions: 0.22(w) x 9.00(h) x 6.00(d)

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