Download or read book An Algorithm for Generalized Matrix Eigenvalue Problems written by C.B. Moler, C.W. Stewart and published by . This book was released on 1972 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Methods for General and Structured Eigenvalue Problems written by Daniel Kressner and published by Springer Science & Business Media. This book was released on 2006-01-20 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about computing eigenvalues, eigenvectors, and invariant subspaces of matrices. Treatment includes generalized and structured eigenvalue problems and all vital aspects of eigenvalue computations. A unique feature is the detailed treatment of structured eigenvalue problems, providing insight on accuracy and efficiency gains to be expected from algorithms that take the structure of a matrix into account.
Download or read book The Matrix Eigenvalue Problem written by David S. Watkins and published by SIAM. This book was released on 2007-01-01 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first in-depth, complete, and unified theoretical discussion of the two most important classes of algorithms for solving matrix eigenvalue problems: QR-like algorithms for dense problems and Krylov subspace methods for sparse problems. The author discusses the theory of the generic GR algorithm, including special cases (for example, QR, SR, HR), and the development of Krylov subspace methods. This book also addresses a generic Krylov process and the Arnoldi and various Lanczos algorithms, which are obtained as special cases. Theoretical and computational exercises guide students, step by step, to the results. Downloadable MATLAB programs, compiled by the author, are available on a supplementary Web site. Readers of this book are expected to be familiar with the basic ideas of linear algebra and to have had some experience with matrix computations. Ideal for graduate students, or as a reference book for researchers and users of eigenvalue codes.
Download or read book An Algorithm for the Generalized Matrix Eigenvalue Problem written by Stanford University. Computer Science Department and published by . This book was released on 1971 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Templates for the Solution of Algebraic Eigenvalue Problems written by Zhaojun Bai and published by SIAM. This book was released on 2000-01-01 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book An Extension of the QZ Algorithm for Solving the Generalized Matrix Eigenvalue Problem written by Robert Cleveland Ward and published by . This book was released on 1973 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: This algorithm is an extension of Moler and Stewart's QZ algorithm with some added features for saving time and operations. Also, some additional properties of the QR algorithm which were not practical to implement in the QZ algorithm can be generalized with the combination shift QZ algorithm. Numerous test cases are presented to give practical application tests for algorithm. Based on results, this algorithm should be preferred over existing algorithms which attempt to solve the class of generalized eigenproblems where both matrices are singular or nearly singular.
Download or read book Approximate Solution of Non Symmetric Generalized Eigenvalue Problems and Linear Matrix Equations on HPC Platforms written by Martin K"ohler and published by Logos Verlag Berlin GmbH. This book was released on 2022-01-18 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: The solution of the generalized eigenvalue problem is one of the computationally most challenging operations in the field of numerical linear algebra. A well known algorithm for this purpose is the QZ algorithm. Although it has been improved for decades and is available in many software packages by now, its performance is unsatisfying for medium and large scale problems on current computer architectures. In this thesis, a replacement for the QZ algorithm is developed. The design of the new spectral divide and conquer algorithms is oriented towards the capabilities of current computer architectures, including the support for accelerator devices. The thesis describes the co-design of the underlying mathematical ideas and the hardware aspects. Closely connected with the generalized eigenvalue value problem, the solution of Sylvester-like matrix equations is the concern of the second part of this work. Following the co-design approach, introduced in the first part of this thesis, a flexible framework covering (generalized) Sylvester, Lyapunov, and Stein equations is developed. The combination of the new algorithms for the generalized eigenvalue problem and the Sylvester-like equation solves problems within an hour, whose solution took several days incorporating the QZ and the Bartels-Stewart algorithm.
Download or read book An Extension of the QZ Algorithm for Sollving the Generalized written by R.C. Ward and published by . This book was released on 1973 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Inverse Eigenvalue Problems written by Moody Chu and published by Oxford University Press. This book was released on 2005-06-16 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Inverse eigenvalue problems arise in a remarkable variety of applications and associated with any inverse eigenvalue problem are two fundamental questions--the theoretical issue of solvability and the practical issue of computability. Both questions are difficult and challenging. In this text, the authors discuss the fundamental questions, some known results, many applications, mathematical properties, a variety of numerical techniques, as well as several open problems.This is the first book in the authoritative Numerical Mathematics and Scientific Computation series to cover numerical linear algebra, a broad area of numerical analysis. Authored by two world-renowned researchers, the book is aimed at graduates and researchers in applied mathematics, engineering and computer science and makes an ideal graduate text.
Download or read book Algorithms for Selected Matrix Inversion and Generalized Eigenvalue Problems and Their Applications written by Chengming Jiang and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of two parts: a selected matrix inversion algorithm and its application for quantum Monte Carlo simulations, and a generalized eigenvalue problem and its applications for constrained image segmentation and transductive learning. In the first part, we present a fast selected inversion (FSI) algorithm for computing selected blocks of the inverse of a p-cyclic matrix. The FSI algorithm rests on three ideas: applying a structure-preserving block cyclic reduction, computing the inverse of the reduced block p-cyclic matrix by a structured orthogonal factorization, and using the block entries of the inverse of the reduced block p-cyclic matrix as seeds to rapidly form the selected inversion in parallel. The FSI algorithm is implemented using hybrid OpenMP/MPI programming. Performance results of the FSI algorithm show an 80% improvement compared to multi-threaded MKL-based implementation on the Intel "Ivy Bridge'' processor. By embedding the parallel FSI into quantum Monte Carlo (QMC) simulations, it reduces the running time of the multi-threaded MKL-based version by a factor of 5 on the "Ivy Bridge'' processor. In the second part, we propose an algorithm to solve a generalized eigenvalue problem with a pair of positive semi-definite matrices that share a common nullspace. We propose a spectral regularization scheme. We prove that the smallest finite eigenvalue of the matrix pair is the minimum of the Rayleigh quotient by a generalization of Courant-Fischer variational principle. These results address critical unsolved issues of FAST-GE, a generalized spectral method for constrained clustering. The essence of our approach is about mathematically rigorous and computationally effective treatments of symmetric positive semi-definite pencils. We demonstrate the robustness and efficiency of the proposed algorithm for applications in constrained image segmentation and transductive learning.
Download or read book Large Scale Eigenvalue Problems written by J. Cullum and published by Elsevier. This book was released on 1986-01-01 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Results of research into large scale eigenvalue problems are presented in this volume. The papers fall into four principal categories:novel algorithms for solving large eigenvalue problems, novel computer architectures, computationally-relevant theoretical analyses, and problems where large scale eigenelement computations have provided new insight.
Download or read book Core Chasing Algorithms for the Eigenvalue Problem written by Jared L. Aurentz and published by SIAM. This book was released on 2018-07-06 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: Eigenvalue computations are ubiquitous in science and engineering. John Francis?s implicitly shifted QR algorithm has been the method of choice for small to medium sized eigenvalue problems since its invention in 1959. This book presents a new view of this classical algorithm. While Francis?s original procedure chases bulges, the new version chases core transformations, which allows the development of fast algorithms for eigenvalue problems with a variety of special structures. This also leads to a fast and backward stable algorithm for computing the roots of a polynomial by solving the companion matrix eigenvalue problem. The authors received a SIAM Outstanding Paper prize for this work. This book will be of interest to researchers in numerical linear algebra and their students.
Download or read book ARPACK Users Guide written by Richard B. Lehoucq and published by SIAM. This book was released on 1998-01-01 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a guide to understanding and using the software package ARPACK to solve large algebraic eigenvalue problems. The software described is based on the implicitly restarted Arnoldi method, which has been heralded as one of the three most important advances in large scale eigenanalysis in the past ten years. The book explains the acquisition, installation, capabilities, and detailed use of the software for computing a desired subset of the eigenvalues and eigenvectors of large (sparse) standard or generalized eigenproblems. It also discusses the underlying theory and algorithmic background at a level that is accessible to the general practitioner.
Download or read book The LZ Algorithm to Solve the Generalized Eigenvalue Problem written by Linda Carol Kaufman and published by . This book was released on 1973 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Solving the Large Sparse Generalized Eigenvalue Problem written by John A. Wisniewski and published by . This book was released on 1981 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
