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Author : Kenneth R. Garren
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.:/5 (31 download)
Download or read book Bounds for the Eigenvalues of a Matrix written by Kenneth R. Garren and published by . This book was released on 1968 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Kenneth R. Garren
Publisher :
ISBN 13 :
Total Pages : 158 pages
Book Rating : 4.:/5 (663 download)
Download or read book Bounds for the Eigenvalues of a Matrix written by Kenneth R. Garren and published by . This book was released on 1965 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rajendra Bhatia
Publisher : SIAM
ISBN 13 : 9780898719079
Total Pages : 191 pages
Book Rating : 4.7/5 (19 download)
Download or read book Perturbation Bounds for Matrix Eigenvalues written by Rajendra Bhatia and published by SIAM. This book was released on 1987-01-01 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Perturbation Bounds for Matrix Eigenvalues contains a unified exposition of spectral variation inequalities for matrices. The text provides a complete and self-contained collection of bounds for the distance between the eigenvalues of two matrices, which could be arbitrary or restricted to special classes. The book emphasizes sharp estimates, general principles, elegant methods, and powerful techniques. For the SIAM Classics edition, the author has added over 60 pages of new material, which includes recent results and discusses the important advances made in the theory, results, and proof techniques of spectral variation problems in the two decades since the book's original publication. Audience: physicists, engineers, computer scientists, and mathematicians interested in operator theory, linear algebra, and numerical analysis. The text is also suitable for a graduate course in linear algebra or functional analysis.
Author : Yousef Saad
Publisher : SIAM
ISBN 13 : 9781611970739
Total Pages : 292 pages
Book Rating : 4.9/5 (77 download)
Download or read book Numerical Methods for Large Eigenvalue Problems written by Yousef Saad and published by SIAM. This book was released on 2011-01-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.
Author : Dario A. Bini
Publisher : Birkhäuser
ISBN 13 : 3319491822
Total Pages : 740 pages
Book Rating : 4.3/5 (194 download)
Download or read book Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics written by Dario A. Bini and published by Birkhäuser. This book was released on 2017-03-21 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of expository and research papers on various topics in matrix and operator theory, contributed by several experts on the occasion of Albrecht Böttcher’s 60th birthday. Albrecht Böttcher himself has made substantial contributions to the subject in the past. The book also includes a biographical essay, a complete bibliography of Albrecht Böttcher’s work and brief informal notes on personal encounters with him. The book is of interest to graduate and advanced undergraduate students majoring in mathematics, researchers in matrix and operator theory as well as engineers and applied mathematicians.
Author : Alston S. Householder
Publisher : Courier Corporation
ISBN 13 : 0486145638
Total Pages : 274 pages
Book Rating : 4.4/5 (861 download)
Download or read book The Theory of Matrices in Numerical Analysis written by Alston S. Householder and published by Courier Corporation. This book was released on 2013-06-18 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents selected aspects of matrix theory that are most useful in developing computational methods for solving linear equations and finding characteristic roots. Topics include norms, bounds and convergence; localization theorems; more. 1964 edition.
Author : D.M. Cvetkovic
Publisher : Elsevier
ISBN 13 : 9780080867762
Total Pages : 305 pages
Book Rating : 4.8/5 (677 download)
Download or read book Recent Results in the Theory of Graph Spectra written by D.M. Cvetkovic and published by Elsevier. This book was released on 1988-01-01 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this volume is to review the results in spectral graph theory which have appeared since 1978. The problem of characterizing graphs with least eigenvalue -2 was one of the original problems of spectral graph theory. The techniques used in the investigation of this problem have continued to be useful in other contexts including forbidden subgraph techniques as well as geometric methods involving root systems. In the meantime, the particular problem giving rise to these methods has been solved almost completely. This is indicated in Chapter 1. The study of various combinatorial objects (including distance regular and distance transitive graphs, association schemes, and block designs) have made use of eigenvalue techniques, usually as a method to show the nonexistence of objects with certain parameters. The basic method is to construct a graph which contains the structure of the combinatorial object and then to use the properties of the eigenvalues of the graph. Methods of this type are given in Chapter 2. Several topics have been included in Chapter 3, including the relationships between the spectrum and automorphism group of a graph, the graph isomorphism and the graph reconstruction problem, spectra of random graphs, and the Shannon capacity problem. Some graph polynomials related to the characteristic polynomial are described in Chapter 4. These include the matching, distance, and permanental polynomials. Applications of the theory of graph spectra to Chemistry and other branches of science are described from a mathematical viewpoint in Chapter 5. The last chapter is devoted to the extension of the theory of graph spectra to infinite graphs.
Author : Joel Tropp
Publisher :
ISBN 13 : 9781601988386
Total Pages : 256 pages
Book Rating : 4.9/5 (883 download)
Download or read book An Introduction to Matrix Concentration Inequalities written by Joel Tropp and published by . This book was released on 2015-05-27 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. It is therefore desirable to have tools for studying random matrices that are flexible, easy to use, and powerful. Over the last fifteen years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that achieve all of these goals. This monograph offers an invitation to the field of matrix concentration inequalities. It begins with some history of random matrix theory; it describes a flexible model for random matrices that is suitable for many problems; and it discusses the most important matrix concentration results. To demonstrate the value of these techniques, the presentation includes examples drawn from statistics, machine learning, optimization, combinatorics, algorithms, scientific computing, and beyond.
Author : Zoran Stanić
Publisher : Cambridge University Press
ISBN 13 : 1107545978
Total Pages : 311 pages
Book Rating : 4.1/5 (75 download)
Download or read book Inequalities for Graph Eigenvalues written by Zoran Stanić and published by Cambridge University Press. This book was released on 2015-07-23 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the inequalities for eigenvalues of the six matrices associated with graphs. Includes the main results and selected applications.
Author : Francoise Chatelin
Publisher : SIAM
ISBN 13 : 1611972450
Total Pages : 428 pages
Book Rating : 4.6/5 (119 download)
Download or read book Eigenvalues of Matrices written by Francoise Chatelin and published by SIAM. This book was released on 2013-01-03 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and accessible guide to the calculation of eigenvalues of matrices, ideal for undergraduates, or researchers/engineers in industry.
Author : Michael Gil'
Publisher : CRC Press
ISBN 13 : 1498796915
Total Pages : 224 pages
Book Rating : 4.4/5 (987 download)
Download or read book Bounds for Determinants of Linear Operators and their Applications written by Michael Gil' and published by CRC Press. This book was released on 2017-03-03 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the determinants of linear operators in Euclidean, Hilbert and Banach spaces. Determinants of operators give us an important tool for solving linear equations and invertibility conditions for linear operators, enable us to describe the spectra, to evaluate the multiplicities of eigenvalues, etc. We derive upper and lower bounds, and perturbation results for determinants, and discuss applications of our theoretical results to spectrum perturbations, matrix equations, two parameter eigenvalue problems, as well as to differential, difference and functional-differential equations.
Author : Alston Scott Householder
Publisher :
ISBN 13 :
Total Pages : 552 pages
Book Rating : 4.F/5 ( download)
Download or read book KWIC Index for Numerical Algebra written by Alston Scott Householder and published by . This book was released on 1972 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert M. Gray
Publisher : Now Publishers Inc
ISBN 13 : 1933019239
Total Pages : 105 pages
Book Rating : 4.9/5 (33 download)
Download or read book Toeplitz and Circulant Matrices written by Robert M. Gray and published by Now Publishers Inc. This book was released on 2006 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes. The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes.
Author : Beresford N. Parlett
Publisher : SIAM
ISBN 13 : 9781611971163
Total Pages : 422 pages
Book Rating : 4.9/5 (711 download)
Download or read book The Symmetric Eigenvalue Problem written by Beresford N. Parlett and published by SIAM. This book was released on 1998-01-01 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to Parlett, "Vibrations are everywhere, and so too are the eigenvalues associated with them. As mathematical models invade more and more disciplines, we can anticipate a demand for eigenvalue calculations in an ever richer variety of contexts." Anyone who performs these calculations will welcome the reprinting of Parlett's book (originally published in 1980). In this unabridged, amended version, Parlett covers aspects of the problem that are not easily found elsewhere. The chapter titles convey the scope of the material succinctly. The aim of the book is to present mathematical knowledge that is needed in order to understand the art of computing eigenvalues of real symmetric matrices, either all of them or only a few. The author explains why the selected information really matters and he is not shy about making judgments. The commentary is lively but the proofs are terse. The first nine chapters are based on a matrix on which it is possible to make similarity transformations explicitly. The only source of error is inexact arithmetic. The last five chapters turn to large sparse matrices and the task of making approximations and judging them.
Author : Ravindra B. Bapat
Publisher : Springer
ISBN 13 : 1447165691
Total Pages : 197 pages
Book Rating : 4.4/5 (471 download)
Download or read book Graphs and Matrices written by Ravindra B. Bapat and published by Springer. This book was released on 2014-09-19 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.
Author : Rajendra Bhatia
Publisher : Springer Science & Business Media
ISBN 13 : 1461206537
Total Pages : 360 pages
Book Rating : 4.4/5 (612 download)
Download or read book Matrix Analysis written by Rajendra Bhatia and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a substantial part of matrix analysis that is functional analytic in spirit. Topics covered include the theory of majorization, variational principles for eigenvalues, operator monotone and convex functions, and perturbation of matrix functions and matrix inequalities. The book offers several powerful methods and techniques of wide applicability, and it discusses connections with other areas of mathematics.
Author : Ravindran Kannan
Publisher : Now Publishers Inc
ISBN 13 : 1601982747
Total Pages : 153 pages
Book Rating : 4.6/5 (19 download)
Download or read book Spectral Algorithms written by Ravindran Kannan and published by Now Publishers Inc. This book was released on 2009 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well as "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, and novel algorithms for estimating spectral parameters. The first part of the book presents applications of spectral methods to problems from a variety of topics including combinatorial optimization, learning and clustering. The second part of the book is motivated by efficiency considerations. A feature of many modern applications is the massive amount of input data. While sophisticated algorithms for matrix computations have been developed over a century, a more recent development is algorithms based on "sampling on the fly" from massive matrices. Good estimates of singular values and low rank approximations of the whole matrix can be provably derived from a sample. The main emphasis in the second part of the book is to present these sampling methods with rigorous error bounds. It also presents recent extensions of spectral methods from matrices to tensors and their applications to some combinatorial optimization problems.
