**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...