#### ACM Transactions on Mathematical Software (TOMS), Volume 12 Issue 4, Dec. 1986

**On computational efficiency of the iterative methods for the simultaneous approximation of polynomial zeros**

G. V. Milovanovic, M. S. Petkovic

Pages: 295-306

DOI: 10.1145/22721.8932

A measure of efficiency of simultaneous methods for determination of polynomial zeros, defined by the coefficient of efficiency, is considered. This coefficient takes into consideration (1) the R-order of convergence in the sense of the...

**Implementation aids for optimization algorithms that solve sequences of linear programs**

J. L. Nazareth

Pages: 307-323

DOI: 10.1145/22721.22959

We describe a collection of modules designed to facilitate the implementation of optimization (LP) algorithms that must solve one or more linear programs in a suitably coordinated sequence. Our collection also provides a basis for discussing...

**Transforming FORTRAN DO loops to improve performance on vector architectures**

Wayne R. Cowell, Christopher P. Thompson

Pages: 324-353

DOI: 10.1145/22721.24035

The performance of programs executing on vector computers is significantly improved when the number of accesses to memory can be reduced. Unrolling Fortran DO loops, followed by substitutions and eliminations in the unrolled code, can reduce the...

**The solution of a combustion problem with Rosenbrock methods**

A. Ostermann, P. Kaps, T. D. Bui

Pages: 354-361

DOI: 10.1145/22721.22722

Solving flame propagation problems with the method of lines leads to large systems of ordinary differential equations. These systems are usually solved by Backward Differentiation Formula (BDF) methods, such as by LSODE of Hindmarsh. Recently,...

**Algorithm 647: Implementation and Relative Efficiency of Quasirandom Sequence Generators**

Bennett L. Fox

Pages: 362-376

DOI: 10.1145/22721.356187

**Computation of the incomplete gamma function ratios and their inverse**

Armido R DiDonato, Alfred H Morris, Jr.

Pages: 377-393

DOI: 10.1145/22721.23109

An algorithm is given for computing the incomplete gamma function ratios P(a, x) and Q>(a, x) for a ⪈ 0,...