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【分享】[PDF]The Theory of Matrices in Numerical Analysis.1964[New]
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The Theory of Matrices in Numerical Analysis 本资源来自于互联网，仅供学习研究之用，不可涉及任何商业用途，请在下载后24小时内删除。 著作权归原作者或出版社所有。未经发贴人conanwj许可，严禁任何人以任何形式转贴本文，违者必究！ Authors(Editors): Alston S. Householder Publisher: Dover Pub Date: 1964 Pages: 270 ISBN: 0-486-61781-5 Preface This book represents an effort to select and present certain aspects of the theory of matrices that are most useful in developing and appraising computational methods for solving systems of linear equations (including the inversion of matrices) and for finding characteristic roots. The solution of linear inequalities and the problems of linear programing are not explicitly considered since there are special difficulties inherent in these problems that are largely combinatorial in character and require a quite different approach. The list of titles at the end of the book should provide convincing evidence that the problems that are treated here are of considerable interest to numerical analysts, and also to mathematicians. This list is culled from perhaps twice as many titles contained in the author's files: these files are certainly not complete, and the number of publications grows at an accel. erating rate. The reason is clear. A finite digital computer can be applied to the solution of functional equations and infinite systems only when finite approximations have been made; and usually the first step toward solving a :p.onlinear system is to linearize. Thus finite linear systems stand at the heart of all mathematical computation. Moreover as science and technology develop, and computers become more powerful, systems to be handled become larger and require techniques that are more refined and efficient. The purpose here is not to develop specific computational layouts or flowcharts, nor is much done explicitly in the way of operational counts or error analysis. These can be found elsewhere in the literature and some specific references will be made in the appropriate places, but particular mention can be made here of papers and forthcoming books by J. H. Wilkinson. In this book the first chapter develops a variety of notions, many classical but not often emphasized in the literature, which will be applied in the subsequent chapters. Chapter 2 develops the theory of norms which plays an increasingly important role in all error analysis and elsewhere. Chapter 3 makes immediate application to localization theorems, important in providing bounds for errors in characteristic roots, and develops some other useful results. The last four chapters survey the known methods, attempting to show the mathematical principles that underlie them, and the mathematical relations among them. It has been assumed that the reader is familiar with the general principles of matrix algebra: addition, subtraction, multiplication, and inversion; the Cayley-Hamilton theorem, characteristic roots and vectors, and normal forms; and the related notions of a vector space, linear dependence, rank, and the like. An outline of this theory can be found in Householder (1953); fuller development can be found in Birkhoff and MacLane (1953), in MacDuffee (1943), and in many other standard text books. However, the Lanczos algorithm as developed in Chapter 1 provides a proof of the CayleyHamilton theorem; and the contents of Chapter 6 provide constructive derivations of some of the normal forms. The author is indebted to many people who have contributed in many ways to this book. At the risk of doing an injustice to others who are not named, he would like to mention in particular R. C. F. Bartels, F. L. Bauer, Ky Fan, George Forsythe, Hans Schneider, R. S. Varga, and J. H. Wilkinson. Their comments, criticisms, suggestions, and encouragement, whether by correspoIidence, by conversation, or both, have been most helpful and stimulating. Grateful acknowledgment is made also to J.\tIae Gill and Barbara Luttrell for the painstaking job of typing. 本资源免费奉送，共6个可选网络硬盘链接，24.9 MB。 -------------------------------------------------------------------------------------------------------- The Theory of Matrices in Numerical Analysis.Alston S. Householder.Dover.1964 The Theory of Matrices in Numerical Analysis.Alston S. Householder.Dover.1964 The Theory of Matrices in Numerical Analysis.Alston S. Householder.Dover.1964 The Theory of Matrices in Numerical Analysis.Alston S. Householder.Dover.1964 The Theory of Matrices in Numerical Analysis.Alston S. Householder.Dover.1964 The Theory of Matrices in Numerical Analysis.Alston S. Householder.Dover.1964 -------------------------------------------------------------------------------------------------------- |
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