Excerpt from On Some Iterative Methods for Solving Elliptic Difference Equations The theorems are used to define three subclasses, called complete image classes, of the general family. These classes contain many of the schemes in current use as well as generalizations of them. Thus it is shown that a variety of independently proposed and seemingly unrelated iterative methods are special cases of a general class of methods. These complete image classes are such that each of the eigenvalues of any scheme in the class is a ...
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Excerpt from On Some Iterative Methods for Solving Elliptic Difference Equations The theorems are used to define three subclasses, called complete image classes, of the general family. These classes contain many of the schemes in current use as well as generalizations of them. Thus it is shown that a variety of independently proposed and seemingly unrelated iterative methods are special cases of a general class of methods. These complete image classes are such that each of the eigenvalues of any scheme in the class is a given algebraic function of at least one of the eigenvalues of a particular reference scheme of the class. Thus a knowledge of the eigenvalues of the reference schemepermits, in principle, the determination of the best scheme of the given class. A special class of equations is considered for which all the eigenvalues of each reference scheme can be explicitly written in terms of the eigenvalues of two matrices. It is then possible to determine which of the reference schemes is best and hence it is also possible to determine that scheme which is best of all those in the complete image classes. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at ... 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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