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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Making static pivoting scalable and dependable
James Demmel,Edward Jason Riedy +1 more
TL;DR: A basic, dependable solver applies to typical dense LU factorization methods using partial pivoting as well as methods that risk greater failure by choosing pivots for nonnumerical reasons, and shows that solutions using these restrictive pivoting methods still have small error.
Journal ArticleDOI
Isotropic distributions of test matrices
Garrett Birkhoff,Surender Gulati +1 more
TL;DR: In this paper, the authors used a special distribution of random matrices as a model for estimating a priori the machine precision needed to solve large linear systems and showed that its matrices are almost never ill-conditioned.
An algorithm for the constrained maximization in nonlinear programming
TL;DR: A continuous version of Rosen's gradient projection method is fully investigated and an algorithm is derived by discretizing the continuous model for numerical computation.
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A constructive method for the solution of the stability problem
TL;DR: In this paper, it is shown that the problem of solving the Liapounov matrix equation is greatly simplified when the real matrix M is in upper Hessenberg form, and the solution is obtained as a linear combinationS = Σp i S i ofn linearly independent symmetric matricesS i, whereS i M +M T S i =2D i and Σ p i D i =?1/2I.
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Well-Conditioned Observer Design for Observer-Based Monitoring Systems
Kunsoo Huh,Jeffrey L. Stein +1 more
TL;DR: A design methodology for synthesizing well-conditioned observers is proposed based on the upper bound of the performance index and it is illustrated with an example that shows that the proposed well- conditioned observer performs much better than an observer designed with traditional pole placement techniques.
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.