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High Performance Algorithms for Structured Matrix Problems

1998 Business & Economics
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Release : 1998
Genre : Business & Economics
Kind : eBook
Book Rating : 947/5 ( reviews)

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Book Synopsis High Performance Algorithms for Structured Matrix Problems by : Peter Arbenz

Download or read book High Performance Algorithms for Structured Matrix Problems written by Peter Arbenz. This book was released on 1998. Available in PDF, EPUB and Kindle. Book excerpt: Comprises 10 contributions that summarize the state of the art in the areas of high performance solutions of structured linear systems and structured eigenvalue and singular-value problems. Topics covered range from parallel solvers for sparse or banded linear systems to parallel computation of eigenvalues and singular values of tridiagonal and bidiagonal matrices. Specific paper topics include: the stable parallel solution of general narrow banded linear systems; efficient algorithms for reducing banded matrices to bidiagonal and tridiagonal form; a numerical comparison of look-ahead Levinson and Schur algorithms for non-Hermitian Toeplitz systems; and parallel CG-methods automatically optimized for PC and workstation clusters. Annotation copyrighted by Book News, Inc., Portland, OR

The Science of High Performance Algorithms for Hierarchical Matrices

2018
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Release : 2018
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Kind : eBook
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Book Synopsis The Science of High Performance Algorithms for Hierarchical Matrices by : Chen-Han Yu (Ph. D.)

Download or read book The Science of High Performance Algorithms for Hierarchical Matrices written by Chen-Han Yu (Ph. D.). This book was released on 2018. Available in PDF, EPUB and Kindle. Book excerpt: Many matrices in scientific computing, statistical inference, and machine learning exhibit sparse and low-rank structure. Typically, such structure is exposed by appropriate matrix permutation of rows and columns, and exploited by constructing an hierarchical approximation. That is, the matrix can be written as a summation of sparse and low-rank matrices and this structure repeats recursively. Matrices that admit such hierarchical approximation are known as hierarchical matrices (H-matrices in brief). H-matrix approximation methods are more general and scalable than solely using a sparse or low-rank matrix approximation. Classical numerical linear algebra operations on H-matrices-multiplication, factorization, and eigenvalue decomposition-can be accelerated by many orders of magnitude. Although the literature on H-matrices for problems in computational physics (low-dimensions) is vast, there is less work for generalization and problems appearing in machine learning. Also, there is limited work on high-performance computing algorithms for pure algebraic H-matrix methods. This dissertation tries to address these open problems on building hierarchical approximation for kernel matrices and generic symmetric positive definite (SPD) matrices. We propose a general tree-based framework (GOFMM) for appropriately permuting a matrix to expose its hierarchical structure. GOFMM supports both static and dynamic scheduling, shared memory and distributed memory architectures, and hardware accelerators. The supported algorithms include kernel methods, approximate matrix multiplication and factorization for large sparse and dense matrices.

Parallel Algorithms for Matrix Computations

1990-01-01 Mathematics
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Release : 1990-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 705/5 ( reviews)

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Book Synopsis Parallel Algorithms for Matrix Computations by : K. Gallivan

Download or read book Parallel Algorithms for Matrix Computations written by K. Gallivan. This book was released on 1990-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Describes a selection of important parallel algorithms for matrix computations. Reviews the current status and provides an overall perspective of parallel algorithms for solving problems arising in the major areas of numerical linear algebra, including (1) direct solution of dense, structured, or sparse linear systems, (2) dense or structured least squares computations, (3) dense or structured eigenvaluen and singular value computations, and (4) rapid elliptic solvers. The book emphasizes computational primitives whose efficient execution on parallel and vector computers is essential to obtain high performance algorithms. Consists of two comprehensive survey papers on important parallel algorithms for solving problems arising in the major areas of numerical linear algebra--direct solution of linear systems, least squares computations, eigenvalue and singular value computations, and rapid elliptic solvers, plus an extensive up-to-date bibliography (2,000 items) on related research.

Advances in the Theory of Computation and Computational Mathematics: High performance algorithms for structured matrix problems

1996 Computer science
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Release : 1996
Genre : Computer science
Kind : eBook
Book Rating : 503/5 ( reviews)

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Book Synopsis Advances in the Theory of Computation and Computational Mathematics: High performance algorithms for structured matrix problems by : Lee L. Keener

Download or read book Advances in the Theory of Computation and Computational Mathematics: High performance algorithms for structured matrix problems written by Lee L. Keener. This book was released on 1996. Available in PDF, EPUB and Kindle. Book excerpt:

Structured Matrices and Polynomials

2001-06-26 Computers
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Release : 2001-06-26
Genre : Computers
Kind : eBook
Book Rating : 402/5 ( reviews)

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Book Synopsis Structured Matrices and Polynomials by : Victor Pan

Download or read book Structured Matrices and Polynomials written by Victor Pan. This book was released on 2001-06-26. Available in PDF, EPUB and Kindle. Book excerpt: Structured matrices serve as a natural bridge between the areas of algebraic computations with polynomials and numerical matrix computations, allowing cross-fertilization of both fields. This book covers most fundamental numerical and algebraic computations with Toeplitz, Hankel, Vandermonde, Cauchy, and other popular structured matrices. Throughout the computations, the matrices are represented by their compressed images, called displacements, enabling both a unified treatment of various matrix structures and dramatic saving of computer time and memory. The resulting superfast algorithms allow further dramatic parallel acceleration using FFT and fast sine and cosine transforms. Included are specific applications to other fields, in particular, superfast solutions to: various fundamental problems of computer algebra; the tangential Nevanlinna--Pick and matrix Nehari problems The primary intended readership for this work includes researchers, algorithm designers, and advanced graduate students in the fields of computations with structured matrices, computer algebra, and numerical rational interpolation. The book goes beyond research frontiers and, apart from very recent research articles, includes yet unpublished results. To serve a wider audience, the presentation unfolds systematically and is written in a user-friendly engaging style. Only some preliminary knowledge of the fundamentals of linear algebra is required. This makes the material accessible to graduate students and new researchers who wish to study the rapidly exploding area of computations with structured matrices and polynomials. Examples, tables, figures, exercises, extensive bibliography, and index lend this text to classroom use or self-study.

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