Journal Article10.1016/0010-4655(89)90164-1
Ordering techniques for the preconditioned conjugate gradient method on parallel computers
Howard C. Elman,Elvira Agrón +1 more
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TL;DR: It is concluded that multicolor orderings result in slower convergence of the preconditioned conjugate gradient method than natural orderings, but that the lower parallel costs of the multicolors typically make their overall performance better.
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About: This article is published in Computer Physics Communications. The article was published on 01 May 1989. The article focuses on the topics: Conjugate residual method & Nonlinear conjugate gradient method.
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Citations
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Iterative Methods for Sparse Linear Systems
Yousef Saad
- 01 Apr 2003
TL;DR: This chapter discusses methods related to the normal equations of linear algebra, and some of the techniques used in this chapter were derived from previous chapters of this book.
Krylov Subspace Methods on Supercomputers
TL;DR: An overview of recent research on Krylov subspace methods with emphasis on implementation on vector and parallel computers and polynomial preconditioning as an alternative to standard incomplete factorization techniques is given.
Fine-Grained Parallel Incomplete LU Factorization
Edmond Chow,Aftab Patel +1 more
TL;DR: Numerical tests show that very few sweeps are needed to construct a factorization that is an effective preconditioner, and the amount of parallelism is large irrespective of the ordering of the matrix, and matrix ordering can be used to enhance the accuracy of the factorization rather than to increase parallelism.
213
AmgX: A Library for GPU Accelerated Algebraic Multigrid and Preconditioned Iterative Methods
Maxim Naumov,M. Arsaev,Patrice Castonguay,Jonathan Cohen,Julien Demouth,Joe Eaton,Simon K. Layton,N. Markovskiy,Istvan Z. Reguly,Nikolai Sakharnykh,V. Sellappan,Robert Strzodka +11 more
TL;DR: The design and implementation of the AmgX library, which provides drop-in GPU acceleration of distributed algebraic multigrid (AMG) and preconditioned iterative methods, is discussed.
158
ILUM: a multi-elimination ILU preconditioner for general sparse matrices
TL;DR: The ILUM factorization described in this paper can be viewed as a multifrontal version of a Gaussian elimination procedure with threshold dropping which has a high degree of potential parallelism.
154
References
Matrix Iterative Analysis
J. H. Bramble,Richard S. Varga +1 more
Abstract: Matrix Properties and Concepts.- Nonnegative Matrices.- Basic Iterative Methods and Comparison Theorems.- Successive Overrelaxation Iterative Methods.- Semi-Iterative Methods.- Derivation and Solution of Elliptic Difference Equations.- Alternating-Direction Implicit Iterative Methods.- Matrix Methods for Parabolic Partial Differential Equations.- Estimation of Acceleration Parameters.
6.8K
•Book
Matrix iterative analysis
Richard S. Varga
- 30 Nov 1961
TL;DR: In this article, the authors propose Matrix Methods for Parabolic Partial Differential Equations (PPDE) and estimate of Acceleration Parameters, and derive the solution of Elliptic Difference Equations.
5.8K
•Book
Numerical methods
Åke Björck,Germund Dahlquist,Ned Anderson +2 more
- 01 Jan 1974
TL;DR: This study investigates the effects of underground structures on wave propagation and surface ground acceleration, employing a nonlinear cyclic model to analyze the impact of input motion, embedment, and dimensions on spectral ratio, peak ground acceleration, and relative displacement under near-fault and far-fault earthquakes.
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An iterative solution method for linear systems of which the coefficient matrix is a symmetric -matrix
TL;DR: A particular class of regular splittings of not necessarily symmetric M-matrices is proposed, if the matrix is symmetric, this splitting is combined with the conjugate-gradient method to provide a fast iterative solution algorithm.
Topological properties of hypercubes
Y. Saad,M.H. Schultz +1 more
TL;DR: The authors examine the hypercube from the graph-theory point of view and consider those features that make its connectivity so appealing and propose a theoretical characterization of the n-cube as a graph.
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