Matrices That Generate the Same Krylov Residual Spaces (Classic Reprint)

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Excerpt from Matrices That Generate the Same Krylov Residual SpacesIf the matrix A is normal, then h'(z) is one, and it was recently shown in several different ways that this bound is sharp, i.e., that for each Is, there is an initial vector (depending on k) for which equality holds in In many cases of interest. However. The matrix A is not normal and the factor in (7) may be quite large. (see. For instance. [13] for some interesting physical examples.) In such cases. The bound (7) may be a large overestimate of the actual residual.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis 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.