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Excerpt from On the Conditioning of the Nonsymmetric Eigenproblem: Theory and Software The condition number of a problem measures the sensitivity of the solution to small changes in the input. We call the problem ill-conditioned if its condition number is large, and ill-posed if its condition number is infinite. We may use condition numbers to bound errors in computed solutions of numerical problems. We illustrate this with a simple example. It is well known that the condition number for solving a system of linear equations is ic(a) E A where [i II is any matrix operator norm (we will be more specific about norms later). Suppose that linear system Ar. B is solved via Gaussian elimination with partial pivoting, or some other stable scheme. Let f be the computed solution. Then one may bound the error by. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

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