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.
Journal ArticleDOI
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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.
Journal ArticleDOI
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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Journal ArticleDOI
Modelling dissipation in harbour resonance
TL;DR: In this paper, the authors extended the theoretical harbor resonance model to include the effects of flow separation and dissipation, and the measured response of Granger Bay harbour prototype, Cape Town, South Africa was used.
Journal ArticleDOI
Gaussian elimination: when is scaling beneficial?
George Poole,Larry Neal +1 more
TL;DR: In this article, the underlying hyperplane geometry of both the sweepout phase and the back-substitution phase of GE is used to achieve a new level of understanding of how scaling or equilibration influences PP in the selection of pivot equations.
Journal ArticleDOI
Methode numerique de detection de la singularite d'une matrice
TL;DR: A numerical method is presented which determines a valueC for the ≪degree of conditioning≫ of a matrix which is 0 for a singular matrix and has progressively larger values for matrices which are increasingly well-conditioned.
Proceedings ArticleDOI
Contribution of a new matrix H-inverse to stabilizing the perfect control for LTI MIMO state-space systems
TL;DR: The SVD-based H- inverse with parameter and polynomial degrees of freedom clearly outperforms the classical minimum-norm right T-inverse in terms of its contribution to stable perfect control design.
Journal ArticleDOI
Evaluation de l'incertitude sur la solution d'un système lineaire
TL;DR: In this paper, the accuracy of linear algebraic systems by numerical method is not easily accomplished on account of the finite precision of computer arithmetic, and they present a numerical method which determines for each variablex i, the numberC i of exact significant figures.