Download or read book The Use of Lanczos s Method to Solve the Large Generalized Symmetric Definite Eigenvalue Problem written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1989 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: The generalized eigenvalue problem, Kx = lambda Mx, is of significant practical importance, especially in structural engineering where it arises as the vibration and buckling problems. A new algorithm, LANZ, based on Lanczos's method is developed. LANZ uses a technique called dynamic shifting to improve the efficiency and reliability of the Lanczos algorithm. A new algorithm for solving the tridiagonal matrices that arise when using Lanczos's method is described. A modification of Parlett and Scott's selective orthogonalization algorithm is proposed. Results from an implementation of LANZ on a Convex C-220 show it to be superior to a subspace iteration code. (KR).
Download or read book The Use of Lanczos s Method to Solve the Large Generalized Symmetric Definite Eigenvalue Problem written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-07-17 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: The generalized eigenvalue problem, Kx = Lambda Mx, is of significant practical importance, especially in structural enginering where it arises as the vibration and buckling problem. A new algorithm, LANZ, based on Lanczos's method is developed. LANZ uses a technique called dynamic shifting to improve the efficiency and reliability of the Lanczos algorithm. A new algorithm for solving the tridiagonal matrices that arise when using Lanczos's method is described. A modification of Parlett and Scott's selective orthogonalization algorithm is proposed. Results from an implementation of LANZ on a Convex C-220 show it to be superior to a subspace iteration code. Jones, Mark T. and Patrick, Merrell L. Unspecified Center...
Download or read book The Use of Lanczos s Method to Solve the Large Generalized Symmetric Definite Eigenvalue Problem written by National Aeronautics and Space Adm Nasa and published by Independently Published. This book was released on 2018-11-06 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: The generalized eigenvalue problem, Kx = Lambda Mx, is of significant practical importance, especially in structural enginering where it arises as the vibration and buckling problem. A new algorithm, LANZ, based on Lanczos's method is developed. LANZ uses a technique called dynamic shifting to improve the efficiency and reliability of the Lanczos algorithm. A new algorithm for solving the tridiagonal matrices that arise when using Lanczos's method is described. A modification of Parlett and Scott's selective orthogonalization algorithm is proposed. Results from an implementation of LANZ on a Convex C-220 show it to be superior to a subspace iteration code. Jones, Mark T. and Patrick, Merrell L. Unspecified Center...
Download or read book The Use of Lanczo s Method to Solve the Large Generalized Symmetric Eigenvalue Problem in Parallel written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1990 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: The generalized eigenvalue problem, Kx=LamdaMx, is of significant practical importance, especially in structural engineering where it arises as the vibration and buckling problems. New software, LANZ, based on Lanczo's method has been developed for solving these problems and uns on SUN 3, SUN 4, Convex C-220, Cray 2, and Cray Y-MP systems. Preliminary results of using the Force to obtain a multiprocessor implementation of LANZ on MIMD parallel/vector systems are reported here. A parallel execution time model of LANZ is defined and used to predict the performance of LANZ as well as examine hypothetical modifications to LANZ. The results of using dynamic shifting to improve parallelism are presented. Finally, the results of assigning a group of processors to separate shifts and finding all the desired eigenvalues using LANZ in parallel are reported. Keywords: Eigenvalues; Parallel orientation; Mathematical methods; Computer software; Computer systems. (cp).
Download or read book Lanczos Algorithms for Large Symmetric Eigenvalue Computations written by Jane K. Cullum and published by SIAM. This book was released on 2002-09-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 1985, this book presents background material, descriptions, and supporting theory relating to practical numerical algorithms for the solution of huge eigenvalue problems. This book deals with 'symmetric' problems. However, in this book, 'symmetric' also encompasses numerical procedures for computing singular values and vectors of real rectangular matrices and numerical procedures for computing eigenelements of nondefective complex symmetric matrices. Although preserving orthogonality has been the golden rule in linear algebra, most of the algorithms in this book conform to that rule only locally, resulting in markedly reduced memory requirements. Additionally, most of the algorithms discussed separate the eigenvalue (singular value) computations from the corresponding eigenvector (singular vector) computations. This separation prevents losses in accuracy that can occur in methods which, in order to be able to compute further into the spectrum, use successive implicit deflation by computed eigenvector or singular vector approximations.
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 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 Proceedings of the Fifth SIAM Conference on Applied Linear Algebra written by John Gregg Lewis and published by SIAM. This book was released on 1994-01-01 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Lanczos Method written by Louis Komzsik and published by SIAM. This book was released on 2003-01-01 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Lanczos Method: Evolution and Application is divided into two distinct parts. The first part reviews the evolution of one of the most widely used numerical techniques in the industry. The development of the method, as it became more robust, is demonstrated through easy-to-understand algorithms. The second part contains industrial applications drawn from the author's experience. These chapters provide a unique interaction between the numerical algorithms and their engineering applications.
Download or read book Lanczos Eigensolution Method for High performance Computers written by and published by . This book was released on 1991 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proceedings of the Cornelius Lanczos International Centenary Conference written by J. David Brown and published by SIAM. This book was released on 1994-01-01 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Sparse Matrix Computations written by James R. Bunch and published by Academic Press. This book was released on 2014-05-10 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sparse Matrix Computations is a collection of papers presented at the 1975 Symposium by the same title, held at Argonne National Laboratory. This book is composed of six parts encompassing 27 chapters that contain contributions in several areas of matrix computations and some of the most potential research in numerical linear algebra. The papers are organized into general categories that deal, respectively, with sparse elimination, sparse eigenvalue calculations, optimization, mathematical software for sparse matrix computations, partial differential equations, and applications involving sparse matrix technology. This text presents research on applied numerical analysis but with considerable influence from computer science. In particular, most of the papers deal with the design, analysis, implementation, and application of computer algorithms. Such an emphasis includes the establishment of space and time complexity bounds and to understand the algorithms and the computing environment. This book will prove useful to mathematicians and computer scientists.
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 Linear Algebra and Applications written by Biswa Nath Datta and published by SIAM. This book was released on 2010-02-04 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: An undergraduate textbook that highlights motivating applications and contains summary sections, examples, exercises, online MATLAB codes and a MATLAB toolkit. All the major topics of computational linear algebra are covered, from basic concepts to advanced topics such as the quadratic eigenvalue problem in later chapters.
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.
