Synopsis
Explore a practical approach to solving structured linear systems from finite difference methods.
This book introduces quasi-tridiagonal matrices and shows how direct methods can efficiently handle boundary value problems that arise when discretizing partial differential equations. It highlights when fast, stable solutions are possible and how to apply these ideas to real-world problems.
Readers will see how certain discretizations lead to special matrix forms and how a structured LU process can reduce computation. The work discusses scenarios where direct methods outperform iterative ones, even for challenging problems like the Tricomi equation. It also presents decomposition criteria and strategies to manage large systems by grouping smaller blocks, reducing the need for many inversions.
- How quasi-tridiagonal matrices arise from finite difference schemes for elliptic, hyperbolic, and mixed-type problems
- Direct solution techniques, including LU-like decompositions and the so-called H-process
- Practical considerations for reducing inversions and improving stability on large grids
- Illustrative applications to Poisson and bi-harmonic equations on rectangular and composite regions
Ideal for readers tackling computational PDEs who seek efficient, theory-backed methods for structured linear systems.
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Quasi-Tridiagonal Matrices and Type-Insensitive Differences Equations
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Paperback. Condition: New. 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. print-on-demand item. Seller Inventory # 9781330199152_0
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QuasiTridiagonal Matrices and TypeInsensitive Differences Equations Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781330199152
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QuasiTridiagonal Matrices and TypeInsensitive Differences Equations Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781330199152
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