Quasi-Tridiagonal Matrices and Type-Insensitive Differences Equations
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
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Condition: New
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Print on Demand. This book details direct methods for solving quasi-tridiagonal matrices and their applications to solving type-insensitive difference equations. These matrices arise in solving finite difference equations of problems for pure elliptic equations and for symmetric positive systems. The author outlines a partitioned decomposition of the matrix into a product of lower and upper triangular matrices, which serves as the foundation of the direct methods proposed. A criterion is given for applying these methods, which may be preferable to iterative methods in certain situations. The author also discusses other methods for special types of matrices involving the inversion of relatively small matrices, extending the applicability of the approach. Through illustrative examples, the book demonstrates the effectiveness of these direct methods for solving boundary problems, such as those involving the Tricomi equation. This book provides valuable insights into solving linear equations arising from finite difference approximations, offering a comprehensive treatment of direct methods and their applications in solving complex problems in applied mathematics and beyond. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.…
Seller Inventory # 9781330199152_0
- Title
- Quasi-Tridiagonal Matrices and Type-Insensitive Differences Equations
- Author
- Samuel Schechter
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1330199154
- ISBN 13
- 9781330199152
- Seller catalogs
- Algebra
The processes described here are, in part, extensions of those described by Karlqvist[4] and Cornock[2]. Furthermore it is shown that the finite difference equations obtained from symmetric positive systems, as defined by K. O. Friedrichs[5], also fall into the class of matrices of the form These include, in addition to pure elliptic or hyperbolic equations, a certain class of boundary problems for equations of mixed type such as the Tricomi equation. Where iterative methods for such problems seem to present difficulties, even when Q is positive definite and symmetric, the direct methods for solving are shown below to be feasible for this larger class of problems.
A criterion is given for the process to apply which is similar to that found for the ldu theorem[3]. It is also shown that when the Mn have the same order p, and the Dn are easily invertible, then the process may be reduced to multiplication of matrices and the inversion of one matrix of order p. This last fact was noted by Corhook[2] for the Poisson and bi-harmonic case.
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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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Forgotten Books publishes hundreds of thousands of rare and classic books.
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.
This text has been digitally restored from a historical edition. Some errors may persist, however we consider it worth publishing due to the work's historical value.
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