#### ACM Transactions on Mathematical Software (TOMS), Volume 16 Issue 2, June 1990

**Integrating network optimization capabilities into a high-level modeling language**

Stavros A. Zenios

Pages: 113-142

DOI: 10.1145/78928.78929

Research in network optimization has reached the stage where large-scale problems-linear or non-linear, pure or generalized-are solved very efficiently with minimal computing resources. Representing such problems for solution on the computer,...

**Chemical equilibrium systems as numerical test problems**

Keith Meintjes, Alexander P. Morgan

Pages: 143-151

DOI: 10.1145/78928.78930

A system of nonlinear equations has been used as a test case by at least two authors. This system is purported to describe the equilibrium of the products of hydrocarbon combustion. The given system does not describe the stated physical problem,...

**Algorithm 681: INTBIS, a portable interval Newton/bisection package**

R. Baker Kearfott, Manuel Novoa, III

Pages: 152-157

DOI: 10.1145/78928.78931

We present a portable software package for finding all real roots of a system of nonlinear equations within a region defined by bounds on the variables. Where practical, the package should find all roots with mathematical certainty. Though based...

**Algorithm 682: Talbot's method of the Laplace inversion problems**

A. Murli, M. Rizzardi

Pages: 158-168

DOI: 10.1145/78928.78932

We describe a FORTRAN implementation, and some related problems, of Talbot's method which numerically solves the inversion problem of almost arbitrary Laplace transforms by means of special contour integration.
The basic idea is to...

**Computation of exponential integrals of a complex argument**

Donald E. Amos

Pages: 169-177

DOI: 10.1145/78928.78933

Previous work on exponential integrals of a real argument has produced a computational algorithm which implements backward recurrence on a three-term recurrence relation (Miller algorithm). The process on which the algorithm is based involves...

**Algorithms 683: a portable FORTRAN subroutine for exponential integrals of a complex argument**

Donald E. Amos

Pages: 178-182

DOI: 10.1145/78928.78934

The algorithm computes exponential integrals En(z) for integer orders n ≥ 1 and complex z in -&pgr; < arg z ≤ &pgr;. Both single...