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.
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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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Journal ArticleDOI
Ranking and Winnowing Gross Earth Data for Inversion and Resolution
TL;DR: In this article, the covariance matrix and the inner product matrix of FrechCt kernels are diagonalized simultaneously to provide greater flexibility and numerical stability in solving inverse problems and calculating tradeoff curves.
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Properties of splines in tension
TL;DR: In this article, the convergence rate of interpolatory tension splines with variable tension was shown to be O( h 4 ) for uniformly bounded tension parameters, where h 4 is the number of points in the spline.
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Eigenproblems associated with the discrete LBB condition for incompressible finite elements
TL;DR: In this paper, the authors examined the discrete eigenstructure of a well-known Lagrange multiplier formulation for linear elasticity or Stokes-flow and showed how the weak incompressibility constraint is reflected in the elementary divisor structure of the eigenproblem whose solution determines the finite element approximation to the natural modes.
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Using Mixed Precision for Sparse Matrix Computations to Enhance the Performance while Achieving 64-bit Accuracy
TL;DR: The approach presented here can apply not only to conventional processors but also to exotic technologies such as Field Programmable Gate Arrays (FPGA), Graphical Processing Units (GPU), and the Cell BE processor.
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Application of differential quadrature to transport processes
Faruk Civan,C.M. Sliepcevich +1 more
TL;DR: In this paper, the authors presented the methodology and numerical solution of problems concerning transport processes via the method of differential quadrature and demonstrated the application of the method is demonstrated by solving a simple one-dimensional, time-dependent (transient) diffusion process involving an irreversible reaction without any flux across the end boundary.