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ACM Transactions on Mathematical Software (TOMS), Volume 13 Issue 3, Sept. 1987

Some tests of generalized bisection
R. Baker Kearfott
Pages: 197-220
DOI: 10.1145/29380.29862
This paper addresses the task of reliably finding approximations to all solutions to a system of nonlinear equations within a region defined by bounds on each of the individual coordinates. Various forms of generalized bisection were proposed...

A fourth-order-accurate Fourier method for the Helmholtz equation in three dimensions
Ronald F. Boisvert
Pages: 221-234
DOI: 10.1145/29380.29863
We present fourth-order-accurate compact discretizations of the Helmholtz equation on rectangular domains in two and three dimensions with any combination of Dirichlet, Neumann, or periodic boundary conditions. The resulting systems of linear...

Algorithm 651: Algorithm HFFT–high-order fast-direct solution of the Helmholtz equation
Ronald F. Boisvert
Pages: 235-249
DOI: 10.1145/29380.214342
HFFT is a software package for solving the Helmholtz equation on bounded two- and three-dimensional rectangular domains with Dirichlet, Neumann, or periodic boundary conditions. The software is the result of combining new fourth-order accurate...

On threshold pivoting in the multifrontal method for sparse indefinite systems
Joseph W. H. Liu
Pages: 250-261
DOI: 10.1145/29380.31331
A simple modification to the numerical pivot selection criteria in the multifrontal scheme of Duff and Reid for sparse symmetric matrix factorization is presented. For a given threshold value, the modification allows a broader choice of block 2...

Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm:

Corrigenda for this article is available here


A. Corana, M. Marchesi, C. Martini, S. Ridella
Pages: 262-280
DOI: 10.1145/29380.29864
A new global optimization algorithm for functions of continuous variables is presented, derived from the “Simulated Annealing” algorithm recently introduced in combinatorial optimization. The algorithm is essentially an...

Algorithm 652: HOMPACK: a suite of codes for globally convergent homotopy algorithms
Layne T. Watson, Stephen C. Billups, Alexander P. Morgan
Pages: 281-310
DOI: 10.1145/29380.214343
There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an...

Algorithm 653: Translation of algorithm 539: PC-BLAS, basic linear algebra subprograms for FORTRAN usage with the INTEL 8087, 80287 numeric data processor
R. J. Hanson, F. T. Krogh
Pages: 311-317
DOI: 10.1145/29380.214346

Algorithm 654: FORTRAN subroutines for computing the incomplete gamma function ratios and their inverse
Armido R. DiDonato, Alfred H. Morris, Jr.
Pages: 318-319
DOI: 10.1145/29380.214348

Corrigendum: “Algorithm 650: efficient square root implementation on the 68000” [ACM Trans. Math. Software 13 (1987), no. 2, 138--151]
Kenneth C. Johnson
Page: 320
DOI: 10.1145/29380.356210