Matrix Algorithms, Volume II: Eigensystems
Matrix Algorithms, Volume II: Eigensystems
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DOI：
10.1137/1.9780898718058
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发表时间：
2001
影响因子：
14.3
通讯作者：
G. Stewart
中科院分区：
文献类型：
--
作者：
G. Stewart
这本书是第二卷在预测五卷调查数值线性代数和矩阵算法。这卷对待密集和大规模的本征值问题的数值解，强调算法和理解它们所需的理论背景。强调深度超过广度，斯图尔特教授详细介绍了更重要的算法的推导和实现。注释和参考部分包含指向其他方法的指针，沿着历史注释。这本书分为两个部分：密集eigenproblems和大型eigenproblems。第一部分介绍了广泛应用的QR算法，并将其应用于广义特征值问题的求解和奇异值分解的计算。第二部分处理Krylov序列的方法，如Lanczos和Arnoldi算法，并提出了一种新的治疗的Jacobi-Davidson方法。本调查中的各卷并非旨在成为百科全书。通过深入处理精心挑选的主题，每一卷都为读者提供了阅读研究文献和实现或修改新算法的理论和实践背景。处理的算法说明了伪代码，已在MATLAB实现测试。
This book is the second volume in a projected five-volume survey of numerical linear algebra and matrix algorithms. This volume treats the numerical solution of dense and large-scale eigenvalue problems with an emphasis on algorithms and the theoretical background required to understand them. Stressing depth over breadth, Professor Stewart treats the derivation and implementation of the more important algorithms in detail. The notes and references sections contain pointers to other methods along with historical comments. The book is divided into two parts: dense eigenproblems and large eigenproblems. The first part gives a full treatment of the widely used QR algorithm, which is then applied to the solution of generalized eigenproblems and the computation of the singular value decomposition. The second part treats Krylov sequence methods such as the Lanczos and Arnoldi algorithms and presents a new treatment of the Jacobi-Davidson method. The volumes in this survey are not intended to be encyclopedic. By treating carefully selected topics in depth, each volume gives the reader the theoretical and practical background to read the research literature and implement or modify new algorithms. The algorithms treated are illustrated by pseudocode that has been tested in MATLAB implementations.