Mathematical Software (TOMS)


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ACM Transactions on Mathematical Software (TOMS), Volume 24 Issue 4, Dec. 1998

Algorithm 786: multiple-precision complex arithmetic and functions
David M. Smith
Pages: 359-367
DOI: 10.1145/293686.293687
This article describes a collection of Fortran routines for multiple-precision complex arithmetic and elementary functions. The package provides good exception handling, flexible input and output, trace features, and results that are almost...

Stiffness detection and estimation of dominant spectrum with explicit Runge-Kutta methods
Kersti Ekeland, Brynjulf Owren, Eivor Øines
Pages: 368-382
DOI: 10.1145/293686.287641
A new stiffness detection scheme based on explicit Runge-Kutta methods is proposed. It uses a Krylov subspace approximation to estimate the eigenvalues of the Jacobian of the differential system. The numerical examples indicate that this...

Remark on algorithm 761
Robert J. Renka, Ron Brown
Pages: 383-385
DOI: 10.1145/293686.293689
Several inprovements to algorithm 761 are presented. The problems corrected consist of (1) the computation of a determinant in subroutine SDLEQN may result in overflow, (2) subroutine SDTRCH may fail to correctly determine the set of boundary...

Algorithm 787: Fortran subroutines for approximate solution of maximum independent set problems using GRASP
Mauricio G. C. Resende, Thomas A. Feo, Stuart H. Smith
Pages: 386-394
DOI: 10.1145/293686.293690
Let G=(V, E) be an undirected graph where V and E are the sets of vertices and edges of G, respectively. A subset of the vertices S V is independent if all of its members are pairwise...

Algorithm 788: automatic boundary integral equation programs for the planar Laplace equation
Kendall Atkinson, Youngmok Jeon
Pages: 395-417
DOI: 10.1145/293686.293692
Algorithms with automatic error control are described for the solution of Laplace's equation on both interior and exterior regions, with both Dirichlet and Neumann boundary conditions. The algorithms are based on standard reformulations of each...

Implementation of Hopf and double-Hopf continuation using bordering methods
W. Govaerts, Yu. A. Kuznetsov, B. Sijnave
Pages: 418-436
DOI: 10.1145/293686.293693
We discuss the computational study of curves of Hopf and double-Hopf points in the software package CONTENT developed at CWI, Amsterdam. These are important points in the numerical study of dynamical systems characterized by the occurrence of...

Recipes for adjoint code construction
Ralf Giering, Thomas Kaminski
Pages: 437-474
DOI: 10.1145/293686.293695
Adjoint models are increasingly being developed for use in meteorology and oceanography. Typical applications are data assimilation, model tuning, sensitivity analysis, and determination of singular vectors. The adjoint model computes the...

SPRINT2D: adaptive software for PDEs
M. Berzins, R. Fairlie, S. V. Pennington, J. M. Ware, L. E. Scales
Pages: 475-499
DOI: 10.1145/293686.293696
SPRINT2D is a set of software tools for solving both steady an unsteady partial differential equations in two-space variables. The software consists of a set of coupled modules for mesh generation, spatial discretization, time integration,...