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ACM Transactions on Mathematical Software (TOMS), Volume 19 Issue 3, Sept. 1993

Template-driven interfaces for numerical subroutines
Jon L. Bentley, Mary F. Fernandez, Brian W. Kernighan, Norman L. Schryer
Pages: 265-287
DOI: 10.1145/155743.155757
This paper describes a set of interfaces for numerical subroutines. Typing a short (often one-line) description allows one to solve problems in application domains including least-squares data fitting, differential equations, minimization, root...

Algorithm 719: Multiprecision translation and execution of FORTRAN programs
David H. Bailey
Pages: 288-319
DOI: 10.1145/155743.155767
This paper describes two Fortran utilities for multiprecision computation. The first is a package of Fortran subroutines that perform a variety of arithmetic operations and transcendental functions on floating point numbers of arbitrarily high...

Algorithm 720: An algorithm for adaptive cubature over a collection of 3-dimensional simplices
Jarle Berntsen, Ronald Cools, Terje O. Espelid
Pages: 320-332
DOI: 10.1145/155743.155785
An adaptive algorithm for computing an approximation to the integral of each element in a vector of functions over a 3-dimensional region covered by simplices is presented. The algorithm is encoded in FORTRAN 77. Locally, a cubature...

On the numerical inversion of Laplace transforms: comparison of three new methods on characteristic problems from applications
Dean G. Duffy
Pages: 333-359
DOI: 10.1145/155743.155788
Three frequently used methods for numerically inverting Laplace transforms are tested on complicated transforms taken from the literature. The first method is a straightforward application of the trapezoidal rule to Bromwich's integral. The...

Mathematical software for Sturm-Liouville problems
Steven Pruess, Charles T. Fulton
Pages: 360-376
DOI: 10.1145/155743.155791
Software is described for the Sturm-Liouville eigenproblem. Eigenvalues, eigenfunctions, and spectral density functions can be estimated with global error control. The method of approximating the coefficients forms the mathematical basis. The...

The computation of eigenvalues and solutions of Mathieu's differential equation for noninteger order
Randall B. Shirts
Pages: 377-390
DOI: 10.1145/155743.155796
Two algorithms for calculating the eigenvalues and solutions of Mathieu's differential equation for noninteger order are described. In the first algorithm, Leeb's method is generalized, expanding the Mathieu equation in Fourier series and...

Algorithm 721: MTIEU1 and MTIEU2: two subroutines to compute eigenvalues and solutions to Mathieu's differential equation for noninteger and integer order
Randall B. Shirts
Pages: 391-406
DOI: 10.1145/155743.155847
Two FORTRAN routines are described which calculate eigenvalues and eigenfunctions of Mathieu's differential equation for noninteger as well as integer order, MTIEU1 uses standard matrix techniques with dimension parameterized to give accuracy in...

QR-like algorithms for the nonsymmetric eigenvalue problem
J. B. Haag, D. S. Watkins
Pages: 407-418
DOI: 10.1145/155743.155849
Hybrid codes that combine elements of the QR and LR algorithms are described. The codes can calculate the eigenvalues and, optionally, eigenvectors of real, nonsymmetric matrices. Extensive tests are presented as evidence that, for certain...

Implementation and computational results for the hierarchical algorithm for making sparse matrices sparser
S. Frank Chang, S. Thomas McCormick
Pages: 419-441
DOI: 10.1145/155743.152620
If A is the (sparse) coefficient matrix of linear-equality constraints, for what nonsingular T is A = TA as sparse as possible, and how can it be efficiently computed? An efficient algorithm for this Sparsity...