Improving Data Re-use in Eigenvalue-related Computations PDF Download
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Author: Greg Henry
Publisher:
ISBN:
Category :
Languages : en
Pages : 346
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Author: Greg Henry
Publisher:
ISBN:
Category :
Languages : en
Pages : 346
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Author: L. S. Blackford
Publisher: SIAM
ISBN: 9780898713978
Category : Mathematics
Languages : en
Pages : 362
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Book Description
ScaLAPACK is an acronym for Scalable Linear Algebra Package or Scalable LAPACK. It is a library of high-performance linear algebra routines for distributed memory message-passing MIMD computers and networks of workstations supporting parallel virtual machine (PVM) and/or message passing interface (MPI). It is a continuation of the LAPACK project, which designed and produced analogous software for workstations, vector supercomputers, and shared memory parallel computers. Both libraries contain routines for solving systems of linear equations, least squares problems, and eigenvalue problems. The goals of both projects are efficiency, scalability, reliability, portability, flexibility, and ease of use. ScaLAPACK includes routines for the solution of dense, band, and tridiagonal linear systems of equations, condition estimation and iterative refinement, for LU and Cholesky factorization, matrix inversion, full-rank linear least squares problems, orthogonal and generalized orthogonal factorizations, orthogonal transformation routines, reductions to upper Hessenberg, bidiagonal and tridiagonal form, reduction of a symmetric-definite/ Hermitian-definite generalized eigenproblem to standard form, the symmetric/Hermitian, generalized symmetric/Hermitian, and nonsymmetric eigenproblem, and the singular value decomposition. Prototype codes are provided for out-of-core linear solvers for LU, Cholesky, and QR, the matrix sign function for eigenproblems, an HPF interface to a subset of ScaLAPACK routines, and SuperLU. Software is available in single-precision real, double-precision real, single-precision complex, and double-precision complex. The software has been written to be portable across a wide range of distributed-memory environments such as the Cray T3, IBM SP, Intel series, TM CM-5, networks of workstations, and any system for which PVM or MPI is available. Each Users' Guide includes a CD-ROM containing the HTML version of the ScaLAPACK Users' Guide, the source code for ScaLAPACK and LAPACK, testing and timing programs, prebuilt versions of the library for a number of computers, example programs, and the full set of LAPACK Working Notes.
Author:
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Category : Electronic journals
Languages : en
Pages : 754
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Author:
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ISBN:
Category : Application software
Languages : en
Pages : 880
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Author: Yousef Saad
Publisher: SIAM
ISBN: 9781611970739
Category : Mathematics
Languages : en
Pages : 292
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Book Description
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.
Author: Greg Henry
Publisher:
ISBN:
Category : Algebras, Linear
Languages : en
Pages : 32
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ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 784
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Author:
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ISBN:
Category : Computer engineering
Languages : en
Pages : 604
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Author: Ken Stanley
Publisher:
ISBN:
Category : Decomposition (Mathematics)
Languages : en
Pages : 398
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Abstract: "The execution time of a symmetric eigendecomposition depends upon the application, the algorithm, the implementation, and the computer. Symmetric eigensolvers are used in a variety of applications, and the requirements of the eigensolver vary from application to application. Many different algorithms can be used to perform a symmetric eigendecompostion [sic], each with differing computational properties. Different implementations of the same algorithm may also have greatly differing computational properties. The computer on which the eigensolver is run not only affects execution time but may favor certain algorithms and implementations over others. This thesis explains the performance of the ScaLAPACK symmetric eigensolver, the algorithms that it uses, and other important algorithms for solving the symmetric eigenproblem on today's fastest computers. We offer advice on how to pick the best eigensolver for particular situations and propose a design for the next ScaLAPACK symmetric eigensolver which will offer greater flexibility and 50% better performance."
Author:
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ISBN:
Category : Computer science
Languages : en
Pages : 36
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