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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Some comments on the solution of linear equations
TL;DR: Computational methods of homogeneous ill-conditioned and singular simultaneous linear equations are discussed in this article, where the authors present a method for computing homogeneous linear equations with singular simultaneous equations.
Journal ArticleDOI
Remarks on the complexity of roundoff analysis
TL;DR: This paper investigates the possibility of mechanizing simple Wilkinson-type roundoff analyses, with limited limitations to the scope of this automation, with the aim of automating roundoff errors in certain types of numerical methods.
Journal ArticleDOI
A fine-grained block ILU scheme on regular structures for GPGPUs
TL;DR: A fine-grained BILU (FGBILU) scheme which is particularly effective on GPGPUs and has been implemented with both OpenACC and CUDA and tested as a block-sparse linear solver on a structured 3D grid.
Journal ArticleDOI
A nodal expansion method for fast reactor calculations in hexagonal geometry
TL;DR: In this paper, a hexagonal geometry extension of the nodal expansion diffusion theory method is presented together with solution and acceleration techniques which have proved effective for 2D and 3D fast reactor calculations.
Book
Interval mathematics : proceedings of the International Symposium, Karlsruhe, West Germany, May 20-24, 1975
TL;DR: Two-sided approximation to solutions of nonlinear operator equations-a comparison of methods from classical analysis, functional analysis, and interval analysis
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.