Download or read book Special Matrices and Their Applications in Numerical Mathematics written by Miroslav Fiedler and published by Courier Corporation. This book was released on 2013-12-01 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised and corrected second edition of a classic on special matrices provides researchers in numerical linear algebra and students of general computational mathematics with an essential reference. 1986 edition.
Download or read book Special matrices and their applications in numerical mathematics written by Miroslav Fiedler and published by Springer. This book was released on 1986-08-31 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an updated translation of a book published in Czech by the SNTL - Publishers of Technical Literature in 1981. In developing this book, it was found reasonable to consider special matrices in general sense and also to include some more or less auxiliary topics that made it possible to present some facts or processes more demonstratively. An example is the graph theory. Chapter 1 contains the definitions of basic concepts of the theory of matrices, and fundamental theorems. The Schur complement is defined here in full generality and using its properties we prove the theorem on the factorization of a partitioned matrix into the product of a lower block triangular matrix with identity diagonal blocks, a block diagonal matrix, and an upper block triangular matrix with identity diagonal blocks. The theorem on the Jordan normal form of a matrix is gi¥en without proof. Chapter 2 is concerned with symmetric and Hermitian matrices. We prove Schur's theorem and, using it, we establish the fundamental theorem describing the factorization of symmetric or Hermitian matrices. Further, the properties of positive definite and positive semidefinite matrices are studied. In the conclusion, Sylvester's law of inertia of quadratic forms and theorems on the singular value decomposition and polar decomposition are proved. Chapter 3 treats the mutual connections between graphs and matrices.
Download or read book Numerical Methods in Matrix Computations written by Åke Björck and published by Springer. This book was released on 2014-10-07 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work.
Download or read book Numerical Matrix Analysis written by Ilse C. F. Ipsen and published by SIAM. This book was released on 2009-07-23 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix analysis presented in the context of numerical computation at a basic level.
Download or read book Matrices Moments and Quadrature with Applications written by Gene H. Golub and published by Princeton University Press. This book was released on 2009-12-07 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first part. Applications addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov regularization. This book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.
Download or read book Matrix Algebra written by James E. Gentle and published by Springer Science & Business Media. This book was released on 2007-07-27 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.
Download or read book Exploiting Hidden Structure in Matrix Computations Algorithms and Applications written by Michele Benzi and published by Springer. This book was released on 2017-01-24 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on special matrices and matrices which are in some sense `near’ to structured matrices, this volume covers a broad range of topics of current interest in numerical linear algebra. Exploitation of these less obvious structural properties can be of great importance in the design of efficient numerical methods, for example algorithms for matrices with low-rank block structure, matrices with decay, and structured tensor computations. Applications range from quantum chemistry to queuing theory. Structured matrices arise frequently in applications. Examples include banded and sparse matrices, Toeplitz-type matrices, and matrices with semi-separable or quasi-separable structure, as well as Hamiltonian and symplectic matrices. The associated literature is enormous, and many efficient algorithms have been developed for solving problems involving such matrices. The text arose from a C.I.M.E. course held in Cetraro (Italy) in June 2015 which aimed to present this fast growing field to young researchers, exploiting the expertise of five leading lecturers with different theoretical and application perspectives.
Download or read book Matrix Analysis and Computations written by Zhong-Zhi Bai and published by SIAM. This book was released on 2021-09-09 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive book is presented in two parts; the first part introduces the basics of matrix analysis necessary for matrix computations, and the second part presents representative methods and the corresponding theories in matrix computations. Among the key features of the book are the extensive exercises at the end of each chapter. Matrix Analysis and Computations provides readers with the matrix theory necessary for matrix computations, especially for direct and iterative methods for solving systems of linear equations. It includes systematic methods and rigorous theory on matrix splitting iteration methods and Krylov subspace iteration methods, as well as current results on preconditioning and iterative methods for solving standard and generalized saddle-point linear systems. This book can be used as a textbook for graduate students as well as a self-study tool and reference for researchers and engineers interested in matrix analysis and matrix computations. It is appropriate for courses in numerical analysis, numerical optimization, data science, and approximation theory, among other topics
Download or read book Matrix Algebra written by James E. Gentle and published by Springer Science & Business Media. This book was released on 2007-08-06 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. This much-needed work presents the relevant aspects of the theory of matrix algebra for applications in statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers numerical linear algebra, beginning with a discussion of the basics of numerical computations, and following up with accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors.
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.
Download or read book Nonnegative Matrices and Applications written by R. B. Bapat and published by Cambridge University Press. This book was released on 1997-03-28 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.
Download or read book Sparse Matrices and Their Uses written by IMA Numerical Analysis Group. Conference and published by . This book was released on 1981 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of papers presented at a conference held at the University of Reading from July 9th to July 11th, 1980. The conference was principally expository, discussing the application of sparse matrix techniques and software to various problem areas. Many papers introduced new research areas, so this volume should appeal to sparse matrix researchers, users of sparse matrix technologies, and scientists and engineers who would like to know more about this expanding field.
Download or read book Structured Matrices in Numerical Linear Algebra written by Dario Andrea Bini and published by Springer. This book was released on 2019-04-08 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers selected contributions presented at the INdAM Meeting Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications, held in Cortona, Italy on September 4-8, 2017. Highlights cutting-edge research on Structured Matrix Analysis, it covers theoretical issues, computational aspects, and applications alike. The contributions, written by authors from the foremost international groups in the community, trace the main research lines and treat the main problems of current interest in this field. The book offers a valuable resource for all scholars who are interested in this topic, including researchers, PhD students and post-docs.
Download or read book Nonnegative Matrices in the Mathematical Sciences written by Abraham Berman and published by Academic Press. This book was released on 2014-05-10 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonnegative Matrices in the Mathematical Sciences provides information pertinent to the fundamental aspects of the theory of nonnegative matrices. This book describes selected applications of the theory to numerical analysis, probability, economics, and operations research. Organized into 10 chapters, this book begins with an overview of the properties of nonnegative matrices. This text then examines the inverse-positive matrices. Other chapters consider the basic approaches to the study of nonnegative matrices, namely, geometrical and combinatorial. This book discusses as well some useful ideas from the algebraic theory of semigroups and considers a canonical form for nonnegative idempotent matrices and special types of idempotent matrices. The final chapter deals with the linear complementary problem (LCP). This book is a valuable resource for mathematical economists, mathematical programmers, statisticians, mathematicians, and computer scientists.
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.
Download or read book Applied Numerical Linear Algebra written by James W. Demmel and published by SIAM. This book was released on 1997-08-01 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive textbook is designed for first-year graduate students from a variety of engineering and scientific disciplines.
Download or read book The Theory of Matrices written by Feliks Ruvimovich Gantmakher and published by . This book was released on 1964 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
