| 书目名称 | Numerical Methods for General and Structured Eigenvalue Problems | | 编辑 | Daniel Kressner | | 视频video | | | 丛书名称 | Lecture Notes in Computational Science and Engineering | | 图书封面 |  | | 描述 | The purpose of this book is to describe recent developments in solving eig- value problems, in particular with respect to the QR and QZ algorithms as well as structured matrices. Outline Mathematically speaking, the eigenvalues of a square matrix A are the roots of its characteristic polynomial det(A??I). An invariant subspace is a linear subspace that stays invariant under the action of A. In realistic applications, it usually takes a long process of simpli?cations, linearizations and discreti- tions before one comes up with the problem of computing the eigenvalues of a matrix. In some cases, the eigenvalues have an intrinsic meaning, e.g., for the expected long-time behavior of a dynamical system; in others they are just meaningless intermediate values of a computational method. The same applies to invariant subspaces, which for example can describe sets of initial states for which a dynamical system produces exponentially decaying states. Computing eigenvalues has a long history, dating back to at least 1846 when Jacobi [172] wrote his famous paper on solving symmetric eigenvalue problems. Detailed historical accounts of this subject can be found in two papers by Golub and van d | | 出版日期 | Book 2005 | | 关键词 | algorithms; computational methods; eigenvalue; matrix product; structured matrix | | 版次 | 1 | | doi | https://doi.org/10.1007/3-540-28502-4 | | isbn_softcover | 978-3-540-24546-9 | | isbn_ebook | 978-3-540-28502-1Series ISSN 1439-7358 Series E-ISSN 2197-7100 | | issn_series | 1439-7358 | | copyright | Springer-Verlag Berlin Heidelberg 2005 |
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发表于 2025-3-21 19:25:55
