#### ACM Transactions on Mathematical Software (TOMS), Volume 11 Issue 1, March 1985

**Integration of a primal simplex network algorithm with a large-scale mathematical programming system**

J. A. Tomlin, J. S. Welch

Pages: 1-11

DOI: 10.1145/3147.3163

In this paper we discuss the implementation of a primal simplex algorithm for network problems in the MPSIII mathematical programming system. Because of the need to interface with the rest of the MPS this implementation is unorthodox, but...

**Evaluation of step directions in optimization algorithms**

William C. Davidon, Jorge Nocedal

Pages: 12-19

DOI: 10.1145/3147.3164

We present a method for comparing that part of optimization algorithms that chooses each step direction. It is an example of a general approach to algorithm evaluation in which one tests specific parts of the algorithm, rather than making...

**Computational implementation of the multivariate Halley method for solving nonlinear systems of equations**

Annie A. M. Cuyt, L. B. Rall

Pages: 20-36

DOI: 10.1145/3147.3162

Cubicaliy convergent iterative methods for the solution of nonlinear systems of the multivariate Halley method, require first and second partial derivatives of the of the functions comprising the system. Automatic differentiation is used to...

**Random sampling with a reservoir**

Jeffrey S. Vitter

Pages: 37-57

DOI: 10.1145/3147.3165

We introduce fast algorithms for selecting a random sample of n records without replacement from a pool of N records, where the value of N is unknown beforehand. The main result of the paper is...

**Algorithm 627**: A FORTRAN subroutine for solving Volterra integral equations

John M. Bownds, Lee Appelbaum

Pages: 58-65

DOI: 10.1145/3147.214314

**Algorithm 628**: An algorithm for constructing canonical bases of polynomial ideals

F. Winkler, B. Buchberger, F. Lichtenberger, H. Rolletschek

Pages: 66-78

DOI: 10.1145/3147.214316