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ACM Transactions on Mathematical Software (TOMS), Volume 14 Issue 1, March 1988

An extended set of FORTRAN basic linear algebra subprograms
Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, Richard J. Hanson
Pages: 1-17
DOI: 10.1145/42288.42291
This paper describes an extension to the set of Basic Linear Algebra Subprograms. The extensions are targeted at matrix-vector operations that should provide for efficient and portable implementations of algorithms for high-performance...

Algorithm 656: an extended set of basic linear algebra subprograms: model implementation and test programs
Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, Richard J. Hanson
Pages: 18-32
DOI: 10.1145/42288.42292

This paper describes a model implementation and test software for the Level 2 Basic Linear Algebra Subprograms (Level 2 BLAS). Level 2 BLAS are targeted at matrix-vector operations with the aim of providing more efficient, but portable,...

Plotting contour surfaces of a function of three variables
Granville Sewell
Pages: 33-41
DOI: 10.1145/42288.42289
A technique is presented for the graphical representation of some contour (level) surfaces of a function of three variables defined by its values on an array of points (xi,...

Algorithm 657: software for plotting contour surfaces of a function of three var
Granville Sewell
Pages: 42-44
DOI: 10.1145/42288.42290

The simultaneous solution and sensitivity analysis of systems described by ordinary differential equations
Jorge R. Leis, Mark A. Kramer
Pages: 45-60
DOI: 10.1145/42288.46156
The methodology for the simultaneous solution of ordinary differential equations and the associated first-order parametric sensitivity equations is presented, and a detailed description of its implementation as a modification of a widely...

Algorithm 658: ODESSA–an ordinary differential equation solver with explicit simultaneous sensitivity analysis
Jorge R. Leis, Mark A. Kramer
Pages: 61-67
DOI: 10.1145/42288.214371
ODESSA is a package of FORTRAN routines for simultaneous solution of ordinary differential equations and the associated first-order parametric sensitivity equations, yielding the ODE solution vector...

Towards efficient implementation of singly-implicit methods
J. C. Butcher
Pages: 68-75
DOI: 10.1145/42288.42341
It has been observed that for problems of low dimension the transformations used in the implementation of singly-implicit Runge-Kutta methods consume an unreasonable share of the total computational costs. Two proposals for reducing these costs...

A routine for converting regression algorithms into corresponding orthogonal regression algorithms
Larry Ammann, John Van Ness
Pages: 76-87
DOI: 10.1145/42288.42342
The routine converts any standard regression algorithm (that calculates both the coefficients and residuals) into a corresponding orthogonal regression algorithm. Thus, a standard, or robust, or...

Algorithm 659: Implementing Sobol's quasirandom sequence generator
Paul Bratley, Bennett L. Fox
Pages: 88-100
DOI: 10.1145/42288.214372
We compare empirically accuracy and speed of low-discrepancy sequence generators of Sobol' and Faure. These generators are useful for multidimensional integration and global optimization. We discuss our implementation of the Sobol'...

Best “ordering” for floating-point addition
T. G. Robertazzi, S. C. Schwartz
Pages: 101-110
DOI: 10.1145/42288.42343
This correspondence examines the influence of the summation order on the numerical accuracy of the resulting sum when the addition is performed using floating-point, finite-precision arithmetic. A simple statistical model is used to find the...

Corrigendum: “An Algorithm for Generating Chi Random Variables”
John F. Monahan
Page: 111
DOI: 10.1145/42288.356228