Produktbild: Parallelism in Matrix Computations
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Parallelism in Matrix Computations

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

12.08.2015

Abbildungen

XXX, 473 p. 58 illus.

Verlag

Springer Netherland

Seitenzahl

473

Maße (L/B/H)

24,1/16/3,3 cm

Gewicht

916 g

Auflage

1st ed. 2016

Sprache

Englisch

ISBN

978-94-017-7187-0

Beschreibung

Rezension

“The exposition of the material is always very clear. The book is written confidently, with the greatest expertise and a remarkable breadth of topics. It should be an excellent resource for a broad audience of applied mathematicians. I would recommended it to all students, engineers and researchers in applied mathematics who wish to learn something about modern parallel techniques for large-scale matrix computation. Kudos to the authors on having produced such a delightful read and a much-needed reference!” (Bruno Carpentieri, Mathematical Reviews, 2017)

“The goal of this book is to provide basic principles for the design of such efficient parallel algorithms for dense and sparse matrices. … The book is intended to be adequate for researchers as well as for advanced graduates.” (Gudula Rünger, zbMATH 1341.65011, 2016)

“This book covers parallel algorithmsfor a wide range of matrix computation problems, ranging from solving systems of linear equations to computing pseudospectra of matrices. … This is a valuable reference book for researchers and practitioners in parallel computing. It includes up-to-date and comprehensive lists of references for various topics. … this book is well written and accurate. I highly recommend it to the parallel computing community … .” (Sanzheng Qiao, Computing Reviews, November, 2015)

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

12.08.2015

Abbildungen

XXX, 473 p. 58 illus.

Verlag

Springer Netherland

Seitenzahl

473

Maße (L/B/H)

24,1/16/3,3 cm

Gewicht

916 g

Auflage

1st ed. 2016

Sprache

Englisch

ISBN

978-94-017-7187-0

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: GPSR Kontakt

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  • Produktbild: Parallelism in Matrix Computations

  • List of Figures.- List of Tables.- List of Algorithms.- Notations used in the book.- Part I Basics.- Parallel Programming Paradigms.- Computational Models.- Principles of parallel programming.- Fundamental kernels.- Vector operations.- Higher level BLAS.- General organization for dense matrix factorizations.- Sparse matrix computations.- Part II Dense and special matrix computations.- Recurrences and triangular systems.- Definitions and examples.- Linear recurrences.- Implementations for a given number of processors.- Nonlinear recurrences.- General linear systems.- Gaussian elimination.- Pair wise pivoting.- Block LU factorization.- Remarks.- Banded linear systems.- LUbased schemes with partial pivoting.- The Spike family of algorithms.- The Spike balance scheme.- A tearing based banded solver.- Tridiagonal systems.- Special linear systems.- Vandermonde solvers.- Banded Toeplitz linear systems solvers.- Symmetric and Anti symmetric Decomposition (SAS).- Rapid elliptic solvers.- Orthogonal factorization and linear least squares problems.- Definitions.- QR factorization via Givens rotations.- QR factorization via Householder reductions.- Gram Schmidt orthogonalization.- Normal equations vs. orthogonal reductions.- Hybrid algorithms when m>n.- Orthogonal factorization of block angular matrices.- Rank deficient linear least squares problems.- The symmetric eigenvalue and singular value problems.- The Jacobi algorithms.- Tridiagonalization based schemes.- Bidiagonalization via Householder reduction.- Part III Sparse matrix computations.- Iterative schemes for large linear systems.- An example.- Classical splitting methods.- Polynomial methods.- Preconditioners.- A tearing based solver for generalized banded preconditioners.- Row projection methods for large non symmetric linear systems.- Multiplicative Schwarz preconditioner with GMRES.- Large symmetric eigenvalue problems.- Computing dominant eigenpairs and spectral transformations.- The Lanczos method.- A block Lanczos approach for solving symmetric perturbed standard eigenvalue problems.- The Davidson methods.- The trace minimization method for the symmetric generalized eigenvalue problem.- The sparse singular value problem.- Part IV Matrix functions and characteristics.- Matrix functions and the determinant.- Matrix functions.- Determinants.- Computing the matrix pseudospectrum.- Grid based methods.- Dimensionality reduction on the domain: Methods based on path following.- Dimensionality reduction on the matrix: Methods based on projection.- Notes.- References.