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 Matrices Moments and Quadrature Applications to Time Dependent Partial Differential Equations written by James V. Lambers and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical solution of a time-dependent PDE generally involves the solution of a stiff system of ODEs arising from spatial discretization of the PDE. There are many methods in the literature for solving such systems, such as exponential propagation iterative (EPI) methods, that rely on Krylov projection to compute matrix function-vector products. Unfortunately, as spatial resolution increases, these products require an increasing number of Krylov projection steps, thus drastically increasing computational expense.
Download or read book Matrices Moments and Quadrature written by Stanford University. Computer Science Department. Scientific Computing and Computational Mathematics Program and published by . This book was released on 1994 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Matrices Moments and Quadrature II Or How to Compute the Norm of the Error in Iterative Methods written by Stanford University. Computer Science Department. Scientific Computing and Computational Mathematics Program and published by . This book was released on 1996 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applied Linear Algebra in Action written by Vasilios Katsikis and published by BoD – Books on Demand. This book was released on 2016-07-06 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present text book contains a collection of six high-quality articles. In particular, this book is devoted to Linear Mathematics by presenting problems in Applied Linear Algebra of general or special interest.
Download or read book Matrix Completions Moments and Sums of Hermitian Squares written by Mihály Bakonyi and published by Princeton University Press. This book was released on 2011-07-18 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intensive research in matrix completions, moments, and sums of Hermitian squares has yielded a multitude of results in recent decades. This book provides a comprehensive account of this quickly developing area of mathematics and applications and gives complete proofs of many recently solved problems. With MATLAB codes and more than 200 exercises, the book is ideal for a special topics course for graduate or advanced undergraduate students in mathematics or engineering, and will also be a valuable resource for researchers. Often driven by questions from signal processing, control theory, and quantum information, the subject of this book has inspired mathematicians from many subdisciplines, including linear algebra, operator theory, measure theory, and complex function theory. In turn, the applications are being pursued by researchers in areas such as electrical engineering, computer science, and physics. The book is self-contained, has many examples, and for the most part requires only a basic background in undergraduate mathematics, primarily linear algebra and some complex analysis. The book also includes an extensive discussion of the literature, with close to 600 references from books and journals from a wide variety of disciplines.
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 413 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 Rays Waves and Scattering written by John A. Adam and published by Princeton University Press. This book was released on 2017-05-30 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas. Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technical material), and several informative appendixes. Provides a panoramic look at wave motion in many different contexts Features problems and exercises throughout Includes numerous appendixes, some on topics not often covered An ideal reference book for practitioners Can also serve as a supplemental text in classical applied mathematics, particularly wave theory and mathematical methods in physics and engineering Accessible to anyone with a strong background in ordinary differential equations, partial differential equations, and functions of a complex variable
Download or read book Formal Verification of Control System Software written by Pierre-Loïc Garoche and published by Princeton University Press. This book was released on 2019-05-14 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: An essential introduction to the analysis and verification of control system software The verification of control system software is critical to a host of technologies and industries, from aeronautics and medical technology to the cars we drive. The failure of controller software can cost people their lives. In this authoritative and accessible book, Pierre-Loïc Garoche provides control engineers and computer scientists with an indispensable introduction to the formal techniques for analyzing and verifying this important class of software. Too often, control engineers are unaware of the issues surrounding the verification of software, while computer scientists tend to be unfamiliar with the specificities of controller software. Garoche provides a unified approach that is geared to graduate students in both fields, covering formal verification methods as well as the design and verification of controllers. He presents a wealth of new verification techniques for performing exhaustive analysis of controller software. These include new means to compute nonlinear invariants, the use of convex optimization tools, and methods for dealing with numerical imprecisions such as floating point computations occurring in the analyzed software. As the autonomy of critical systems continues to increase—as evidenced by autonomous cars, drones, and satellites and landers—the numerical functions in these systems are growing ever more advanced. The techniques presented here are essential to support the formal analysis of the controller software being used in these new and emerging technologies.
Download or read book Semidefinite Optimization and Convex Algebraic Geometry written by Grigoriy Blekherman and published by SIAM. This book was released on 2013-03-21 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to convex algebraic geometry and semidefinite optimization. For graduate students and researchers in mathematics and computer science.
Download or read book Krylov Subspace Methods written by Jörg Liesen and published by Numerical Mathematics and Scie. This book was released on 2013 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes the principles and history behind the use of Krylov subspace methods in science and engineering. The outcome of the analysis is very practical and indicates what can and cannot be expected from the use of Krylov subspace methods, challenging some common assumptions and justifications of standard approaches.
Download or read book TMS 2014 143rd Annual Meeting Exhibition Annual Meeting Supplemental Proceedings written by The Minerals, Metals & Materials Society (TMS) and published by Springer. This book was released on 2016-12-16 with total page 1152 pages. Available in PDF, EPUB and Kindle. Book excerpt: These papers present advancements in all aspects of high temperature electrochemistry, from the fundamental to the empirical and from the theoretical to the applied. Topics involving the application of electrochemistry to the nuclear fuel cycle, chemical sensors, energy storage, materials synthesis, refractory metals and their alloys, and alkali and alkaline earth metals are included. Also included are papers that discuss various technical, economic, and environmental issues associated with plant operations and industrial practices.
Download or read book Quadrature Approximation of Matrix Functions with Applications written by David Royce Martin and published by . This book was released on 2012 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation concerns the development of iterative methods for the approximation of functions of a large matrix, motivated by the development of efficient algorithms for the analysis of large-scale linear discrete ill-posed problems and complex networks. The connection between the Lanczos process and Gauss-type quadrature rules has been exploited for several decades in the development of iterative methods for bounding matrix functions; this work further elaborates on the application of Gauss-type quadrature to matrix computations. In addition, methods based on the singular value decomposition (SVD) and eigenvalue decomposition are presented. First we consider the minimization of a functional over a set of approximate solutions of a linear discrete ill-posed problem, in order to compute confidence intervals for components of the solution of such a problem. Our iterative method, using the link between Lanczos bidiagonalization and quadrature rules to bound certain matrix functions, greatly reduces large-scale work relative to available methods. Next we consider methods based on quadrature rules computed via block Lanczos algorithms. We derive anti-Gauss quadrature rules for the symmetric and nonsymmetric block Lanczos algorithms. These methods are applied to the computation of functions of an adjacency matrix. Moreover, novel quantities are introduced which characterize the nodes of a complex network, and which can be computed cheaply via our block methods. The remaining numerical methods presented rely on bounds based on the use of a partial SVD or partial eigenvalue decomposition of a large matrix. Such methods are competitive when solving many problems with a fixed matrix A but different data vectors. An alternative is provided to the aforementioned quadrature-based algorithm for computing confidence intervals for ill-posed problems, which is favorable when confidence intervals for many components are desired. Regarding complex networks, we use a partial eigenvalue decomposition to bound elements of the exponential of a symmetric adjacency matrix, and develop an algorithm which identifies important nodes in a complex network.
Download or read book Milestones in Matrix Computation The selected works of Gene H Golub with commentaries written by Raymond Chan and published by OUP Oxford. This book was released on 2007-02-22 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text presents and discusses some of the most influential papers in Matrix Computation authored by Gene H. Golub, one of the founding fathers of the field. The collection of 21 papers is divided into five main areas: iterative methods for linear systems, solution of least squares problems, matrix factorizations and applications, orthogonal polynomials and quadrature, and eigenvalue problems. Commentaries for each area are provided by leading experts: Anne Greenbaum, Ake Bjorck, Nicholas Higham, Walter Gautschi, and G. W. (Pete) Stewart. Comments on each paper are also included by the original authors, providing the reader with historical information on how the paper came to be written and under what circumstances the collaboration was undertaken. Including a brief biography and facsimiles of the original papers, this text will be of great interest to students and researchers in numerical analysis and scientific computation.
Download or read book Milestones in Matrix Computation written by Gene Howard Golub and published by Oxford University Press. This book was released on 2007-02-22 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text presents and discusses some of the most influential papers in Matrix Computation authored by Gene H. Golub, one of the founding fathers of the field. Including commentaries by leading experts and a brief biography, this text will be of great interest to students and researchers in numerical analysis and scientific computation.
Download or read book The Theory of Matrices written by Peter Lancaster and published by Academic Press. This book was released on 1985-05-28 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algebra; Determinants, inverse matrices, and rank; Linear, euclidean, and unitary spaces; Linear transformations and matrices; Linear transformations in unitary spaces and simple matrices; The jordan canonical form: a geometric approach; Matrix polynomials and normal forms; The variational method; Functions of matrices; Norms and bounds for eigenvalues; Perturbation theory; Linear matrices equations and generalized inverses; Stability problems; Matrix polynomials; Nonnegative matrices.
Download or read book Modern Discrete Mathematics and Analysis written by Nicholas J. Daras and published by Springer. This book was released on 2018-07-05 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: A variety of modern research in analysis and discrete mathematics is provided in this book along with applications in cryptographic methods and information security, in order to explore new techniques, methods, and problems for further investigation. Distinguished researchers and scientists in analysis and discrete mathematics present their research. Graduate students, scientists and engineers, interested in a broad spectrum of current theories, methods, and applications in interdisciplinary fields will find this book invaluable.
