Synopsis
Explore powerful iteration schemes for solving two‑dimensional elliptic problems and learn how their convergence works.
This book studies how different iterative methods behave when solving two‑dimensional elliptic difference equations. It focuses on schemes that separate coordinates and examines how line, block, and alternating updates affect convergence. Readers will see how a matrix can be partitioned to enable reliable iteration and how eigenvalues govern the rate at which errors shrink.
- Learn how separable line simultaneous, line successive, and alternating direction schemes are constructed and analyzed.
- See how the error matrix is formed and how its eigenvalues determine convergence.
- Discover practical examples and how boundary conditions and problem order influence method behavior.
- Understand the role of matrix structure, including block and tri‑diagonal forms, in guiding efficient computation.
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Simultaneous, Successive and Alternating Direction Iteration Schemes
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Paperback. Condition: New. Print on Demand. This book examines the development of numerical techniques for solving elliptic partial differential equations. The author explores the convergence rates of iteration schemes for solving these equations, focusing on schemes that minimize a quadratic form. The book analyzes various schemes, including simultaneous, successive, and alternating direction schemes. By providing explicit solutions and eigenvalues for each scheme, the author offers a comprehensive understanding of their behavior and effectiveness. The book's mathematical rigor provides a solid foundation for researchers and practitioners working in numerical analysis and scientific computing. Its insights contribute to the field's progress by identifying successful strategies for solving elliptic equations and enhancing the accuracy and efficiency of numerical methods. 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 # 9781332195992_0
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Simultaneous, Successive and Alternating Direction Iteration Schemes Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332195992
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Simultaneous, Successive and Alternating Direction Iteration Schemes Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332195992
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