Download or read book Perturbation Bounds for the Definite Generalized Eigenvalue Problem written by G. W. Stewart and published by . This book was released on 1977 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is shown that a definite problem has a complete system of eigenvectors and its eigenvalues are real. Under perturbations of A and B, the eigenvalues behave like the eigenvalues of a Hermitian matrix in the sense that there is a 1-1 pairing of the eigenvalues with the perturbed eigenvalues and a uniform bound for their differences (in this case in the chordal metric). Perturbation bounds are also developed for eigenvectors and eigenspaces.
Download or read book Optimal Perturbation Bounds for the Hermitian Eigenvalue Problem written by Jesse Louis Barlow and published by . This book was released on 1999 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "There is now a large literature on structured perturbation bounds for eigenvalue problems of the form [formula], where H and M are Hermitian. These results give relative error bounds on the i[superscript th] eigenvalue, [lambda subscript i], of the form [formula], and bound the error in the i[superscript th] eigenvector in terms of the relative gap, [formula]. In general, this theory usually restricts H to be nonsingular and M to be positive definite. We relax this restriction by allowing H to be singular. For our results on eigenvales we allow M to be positive semi-definite and for few results we allow it to be more general. For these problems, for eigenvalues that are not zero or infinity under perturbation, it is possible to obtain local relative error bounds. Thus, a wider class of problems may be characterized by this theory. The theory is applied to the SVD and some of its generalizations. In fact, for structured perturbations, our bound on generalized Hermitian eigenproblems are based upon our bounds for generalized singular value problems. Although it is impossible to give meaningful relative error bounds on eigenvalues that are not bounded away from zero, we show that the error in the subspace associated with those eigenvalues can be characterized meaningfully."
Download or read book Perturbation Theory for the Definite Generalized Eigenvalue Problem written by G. W. Stewart and published by . This book was released on 1976 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper concerns perturbation theory for the generalized eigenvalue problem Ax = lambdaBx where A and B are real symmetric matrices of order n> or = to 3. When B is positive definite, as is usually the case in applications, the problem can be reduced to a symmetric eigenvalue problem for the matrix square root of B times the square root of AB, and the wealth of perturbation theory for symmetric eigenvalue problems can be applied.
Download or read book Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems written by Gilbert W. Stewart and published by . This book was released on 1972 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper describes a technique for obtaining error bounds for certain characteristic subspaces associated with the algebraic eigenvalue problem, the generalized eigenvalue problem, and the singular value decomposition. The method also gives perturbation bounds for isolated eigenvalues and useful information about clusters of eigenvalues. The bounds are obtained from an iterative process for generating the subspaces in question, and one or more steps of the iteration can be used to construct perturbation estimates whose error can be bounded. (Author).
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 G W Stewart written by Misha E. Kilmer and published by Springer Science & Business Media. This book was released on 2010-09-30 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt: Published in honor of his 70th birthday, this volume explores and celebrates the work of G.W. (Pete) Stewart, a world-renowned expert in computational linear algebra. This volume includes: forty-four of Stewart's most influential research papers in two subject areas: matrix algorithms, and rounding and perturbation theory; a biography of Stewart; a complete list of his publications, students, and honors; selected photographs; and commentaries on his works in collaboration with leading experts in the field. G.W. Stewart: Selected Works with Commentaries will appeal to graduate students, practitioners, and researchers in computational linear algebra and the history of mathematics.
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 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Large-scale problems of engineering and scientific computing often require solutions of eigenvalue and related problems. This book gives a unified overview of theory, algorithms, and practical software for eigenvalue problems. It organizes this large body of material to make it accessible for the first time to the many nonexpert users who need to choose the best state-of-the-art algorithms and software for their problems. Using an informal decision tree, just enough theory is introduced to identify the relevant mathematical structure that determines the best algorithm for each problem.
Download or read book Numerical Methods for Large Eigenvalue Problems written by Yousef Saad and published by SIAM. This book was released on 2011-05-26 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised edition discusses numerical methods for computing the 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 Matrix Computations written by Gene H. Golub and published by JHU Press. This book was released on 1996-10-15 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revised and updated, the third edition of Golub and Van Loan's classic text in computer science provides essential information about the mathematical background and algorithmic skills required for the production of numerical software. This new edition includes thoroughly revised chapters on matrix multiplication problems and parallel matrix computations, expanded treatment of CS decomposition, an updated overview of floating point arithmetic, a more accurate rendition of the modified Gram-Schmidt process, and new material devoted to GMRES, QMR, and other methods designed to handle the sparse unsymmetric linear system problem.
Download or read book Perturbation Properties of a Multiple Eigenvalue of the Definite Generalized Eigenvalue Problem written by and published by . This book was released on 1997 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Approximation of Linear Operators written by Francoise Chatelin and published by SIAM. This book was released on 2011-05-26 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: New York: Academic Press, 1983.
Download or read book Numerical Algebra Matrix Theory Differential Algebraic Equations and Control Theory written by Peter Benner and published by Springer. This book was released on 2015-05-09 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on differential-algebraic equations, to which he together with Peter Kunkel made many groundbreaking contributions, are the topic of the chapters in Part III. Besides providing a scientific discussion of Volker Mehrmann's work and its impact on the development of several areas of applied mathematics, the individual chapters stand on their own as reference works for selected topics in the fields of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory.
Download or read book On the Numerical Solution of the Definite Generalized Eigenvalue Problem written by Yiu-Sang Moon and published by Department of Computer Science, University of Toronto. This book was released on 1979 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Exclusion Theorems and the Perturbation Analysis of the Generalized Eigenvalue Problem written by K. W. E. Chu and published by . This book was released on 1985 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Perturbation Theory of Eigenvalue Problems written by Franz Rellich and published by CRC Press. This book was released on 1969 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Matrix Pencils written by B. Kagström and published by Springer. This book was released on 2006-11-15 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt:
