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
Citations
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The nirvana scheme applied to one‐dimensional advection
TL;DR: The NIRVANA project as discussed by the authors developed a nonoscillatory, integrally reconstructed, volume-averaged numerical advection scheme, which is built on an explicit, single-step, forward-in-time update of the cell-average variable, without restrictions on the size of the time step.
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Tolerance and Condition in Regression Computations
TL;DR: In this paper, a tolerance test that does not allow a variable to enter the regression program if its correlation with the previously entered variables exceeds a specified level is introduced to achieve computational stability by assuring that the correlation matrix of the independent variables is not nearly singular.
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Direct solution of large systems of linear equations
TL;DR: A very efficient computer subroutine for the direct solution of large numbers of simultaneous linear equations is presented, which uses Gauss elimination on positive-definite symmetrical systems to solve systems of very large size and bandwidth.
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Simulation of Salt‐Water Interface Motion
TL;DR: A numerical model is presented that solves the partial differential equations describing the motion of salt water and fresh water separated by a sharp interface and shows that the model is in good agreement with an analytical solution, but under severe conditions the Dupuit approximation may be inappropriate.
Journal Article
Stable and Efficient Gaussian Process Calculations
Leslie V. Foster,Alex Waagen,Nabeela Aijaz,Michael Hurley,Apolonio Luis,Joel Rinsky,Chandrika J. Satyavolu,Michael J. Way,P. R. Gazis,Ashok N. Srivastava +9 more
TL;DR: It is demonstrated that there can be numerical instabilities in a well known implementation of the subset of regressors approximation technique, and alternate implementations that have better numerical stability properties and can lead to better predictions are discussed.
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.