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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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.
References
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Parallel shooting method for boundary-value problems: application to the neutron transport equation
José Canosa,H. R. Penafiel +1 more
TL;DR: In this article, a direct method for the solution of the spherical harmonics approximation to the Boltzmann equation for neutron transport in slab geometry is given, where only a minimum number of matrix transformations is performed, the precise number being determined dynamically, efficiently, and in a new way by the program itself in the course of the computation.
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Linear algebra and extended mappings generalise public key cryptographic Knapsack algorithms
TL;DR: The original Merkle-Hellman knapsack algorithm is the most practical of the public key algorithms, but is considered insecure, so improvements have been proposed.
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Network direct methods for discretized PDEs on structured grids
VP Il'in,V Vsevolod Nefedov +1 more
TL;DR: The fast direct methods for solving fiveand nine-point systems of linear algebraic equations are considered, based on the electro-technical triangular-star and star-triangular transformations which preserve the original sparse matrix structure, and the algebraic properties of the methods are investigated.
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Cholesky decomposition of the Hilbert matrix
TL;DR: In this paper, the authors gave analytic expressions for the Cholesky decomposition of the Hilbert matrix H=[1/(j+k−1)]=LDL T, and the inverse matrices.
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A new algorithm for the solution of the linear minimax approximation problem
TL;DR: An efficient approach to the solution of the linear mini-max approximation problem by specifying first a feasible point belonging to the feasible boundary surface and then feasible directions of decreasing values of the objective function are determined.