Mathematical Software (TOMS)


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ACM Transactions on Mathematical Software (TOMS), Volume 15 Issue 1, March 1989

Sparse matrix test problems
I. S. Duff, Roger G. Grimes, John G. Lewis
Pages: 1-14
DOI: 10.1145/62038.62043
We describe the Harwell-Boeing sparse matrix collection, a set of standard test matrices for sparse matrix problems. Our test set comprises problems in linear systems, least squares, and eigenvalue calculations from a wide variety of scientific...

A block 6(4) Runge-Kutta formula for nonstiff initial value problems
J. R. Cash
Pages: 15-28
DOI: 10.1145/62038.62042
A new selection is made for an efficient two-step block Runge-Kutta formula of order 6. The new formula is developed using some of the efficiency criteria recently investigated by Shampine, and as a result, a block formula with much improved...

Algorithm 669: BRKF45: a FORTRAN subroutine for solving first-order systems of nonstiff initial value problems for ordinary differential equations
J. R. Cash
Pages: 29-30
DOI: 10.1145/62038.214388

Algorithm 670: a Runge-Kutta-Nyström code
R. W. Brankin, I. Gladwell, J. R. Dormand, P. J. Prince, W. L. Seward
Pages: 31-40
DOI: 10.1145/62038.69650

Performance evaluation of programs for certain Bessel functions
W. J. Cody, L. Stoltz
Pages: 41-48
DOI: 10.1145/62038.62039
This paper presents methods for performance evaluation of the K Bessel functions. Accuracy estimates are based on comparisons involving the multiplication theorem. Some ideas for checking robustness are also given. The...

Numerical experience with sequential quadratic programming algorithms for equality constrained nonlinear programming
David F. Shanno, Kang Hoh Phua
Pages: 49-63
DOI: 10.1145/62038.62040
Computational experience is given for a sequential quadratic programming algorithm when LaGrange multiplier estimates, Hessian approximations, and merit functions are varied to test for computational efficiency. Indications of areas for further...

An improved primal simplex variant for pure processing networks
Michael D. Chang, Chou-Hong J. Chen, Michael Engquist
Pages: 64-78
DOI: 10.1145/62038.62041
In processing networks, ordinary network constraints are supplemented by proportional flow restrictions on arcs entering or leaving some nodes. This paper describes a new primal partitioning algorithm for solving pure processing networks using a...

Algorithm 671: FARB-E-2D: fill area with bicubics on rectangles—a contour plot program
A. Preusser
Pages: 79-89
DOI: 10.1145/62038.69651
An algorithm plotting contour lines for discrete values zij, given at the nodes of a rectangular mesh is described. A bicubic Hermite polynomial f(x, y) is...