Journal ArticleDOI
Computer Solution of Linear Algebraic Systems. By G. Forsythe and C. B. Moler. Pp. xi, 148. 1967. (Prentice-Hall.)
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This article is published in The Mathematical Gazette.The article was published on 1969-05-01. It has received 489 citations till now.read more
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Rounding-error and perturbation bounds for the Cholesky and LDL T factorizations
Ji-guang Sun,Ji-guang Sun +1 more
TL;DR: The precision of the computed Cholesky and LDL T factorizations is given and componentwise rounding-error and perturbation bounds for the Choleska-T factorizations are derived.
Journal ArticleDOI
Parallel direct linear system solvers -- a survey☆
Ahmed H. Sameh,David J. Kuck +1 more
TL;DR: This paper is a survey of direct parallel algorithms for solving systems of linear equations, and states their resulting speedup over the corresponding sequential algorithms, and evaluates their numerical stability, whenever possible.
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Environment Parameters and Basic Functions for Floating-Point Computation
W. S. Brown,S. I. Feldman +1 more
TL;DR: A language-independent proposal for environment parameters and basic functions for floating-point computation is presented, which can be used to write portable and robust codes that deal intimately with thefloating-point representation.
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Evaluation and enhancements of some control volume finite-element methods—part 1. convection-diffusion problems
TL;DR: In this paper, the authors examined three control volume finite-element methods (CVFEMs) for convection-diffusion problems and found that significant improvements in the accuracy of the solutions can often be obtaine...
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Quadratic convergence in interval arithmetic, part II
William Chuba,Webb Miller +1 more
TL;DR: In this paper, the authors investigated the effect of dependence on the error of one operation in an interval arithmetic procedure and proved the quadratic convergence of the "centered form" and of a method of Hansen and Smith for solving linear algebraic systems.
References
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Singular value decomposition and least squares solutions
Gene H. Golub,C. Reinsch +1 more
TL;DR: The decomposition of A is called the singular value decomposition (SVD) and the diagonal elements of ∑ are the non-negative square roots of the eigenvalues of A T A; they are called singular values.
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Hyperquad simulation and speciation (HySS): a utility program for the investigation of equilibria involving soluble and partially soluble species
TL;DR: Hyperquad simulation and speciation (HySS) as mentioned in this paper is a computer program written for the Windows operating system on personal computers which provides simulating titration curves and a system for providing speciation diagrams.
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What every computer scientist should know about floating-point arithmetic
TL;DR: This paper presents a tutorial on the aspects of floating-point that have a direct impact on designers of computer systems, and concludes with examples of how computer system builders can better support floating point.
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Generalization of backpropagation with application to a recurrent gas market model
TL;DR: This paper will derive a generalization of backpropagation to recurrent systems (which input their own output), such as hybrids of perceptron-style networks and Grossberg/Hopfield networks, and does not require the storage of intermediate iterations to deal with continuous recurrence.
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An algorithm for reducing the bandwidth and profile of a sparse matrix
TL;DR: Extensive testing on finite element matrices indicates that the algorithm typically produces bandwidth and profile which are comparable to those of the commonly-used reverse Cuthill–McKee algorithm, yet requires significantly less computation time.