**Algorithm 709: testing algorithm implementations**

A. G. Buckley

Pages: 375-391

DOI: 10.1145/138351.138378

**Algorithm 710: FORTRAN subroutines for computing the eigenvalues and eigenvectors of a general matrix by reduction to general tridiagonal form**

J. J. Dongarra, G. A. Geist, C. H. Romine

Pages: 392-400

DOI: 10.1145/138351.138352

This paper describes programs to reduce a nonsymmetric matrix to tridiagonal form, to compute the eigenvalues of the tridiagonal matrix, to improve the accuracy of an eigenvalue, and to compute the corresponding eigenvector. The intended purpose...

**Discrete-time optimal control problems with general constraints**

M. E. Fisher, L. S. Jennings

Pages: 401-413

DOI: 10.1145/138351.138356

This paper presents a computational procedure for solving combined discrete-time optimal control and optimal parameter selection problems subject to general constraints. The approach adopted is to convert the problem into a nonlinear programming...

**Algorithm 711: BTN: software for parallel unconstrained optimization**

Stephen G. Nash, Ariela Sofer

Pages: 414-448

DOI: 10.1145/138351.138359

BTN is a collection of FORTRAN subroutines for solving unconstrained nonlinear optimization problems. It currently runs on both Intel hypercube computers (distributed memory) and Sequent computers (shared memory), and can take advantage of...

**A fast normal random number generator**

Joseph L. Leva

Pages: 449-453

DOI: 10.1145/138351.138364

A method is presented for generating pseudorandom numbers with a normal distribution. The technique uses the ratio of uniform deviates method discovered by Kinderman and Monahan with an improved set of bounding curves. An optimized quadratic fit...

**Algorithm 712: A normal random number generator**

Joseph L. Leva

Pages: 454-455

DOI: 10.1145/138351.138367

**Portable vectorized software for Bessel function evaluation**

Ronald F. Boisvert, Bonita V. Saunders

Pages: 456-469

DOI: 10.1145/138351.138370

A suite of computer programs for the evaluation of Bessel functions and modified Bessel functions of orders zero and one for a vector of real arguments is described. Distinguishing characteristics of these programs are that (a) they are portable...

**Computation of the multivariate normal integral**

Zvi Drezner

Pages: 470-480

DOI: 10.1145/138351.138375

This paper presents a direct computation of the multivariate normal integral by the Gauss Quadrature method. An error control method is given. Results are presented for multivariate integrals consisting of up to twelve normal distributions. A...

**Precise computation using range arithmetic, via C++**

Oliver Aberth, Mark J. Schaefer

Pages: 481-491

DOI: 10.1145/138351.138377

An arithmetic is described that can replace floating-point arithmetic for programming tasks requiring assured accuracy. A general explanation is given of how the arithmetic is constructed with C++, and a programming example in this language is...