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ACM Transactions on Mathematical Software (TOMS), Volume 16 Issue 3, Sept. 1990

Accurate and efficient testing of the exponential and logarithm functions
Ping-Tak Peter Tang
Pages: 185-200
DOI: 10.1145/79505.79506
Table-driven techniques can be used to test highly accurate implementation of EXP LOG. The largest error observeed in EXP and LOG accurately to within 1/500 unit in the last place are reported in our tests. Methods to verify the tests'...

A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides
J. R. Cash, Alan H. Karp
Pages: 201-222
DOI: 10.1145/79505.79507
Explicit Runge-Kutta methods (RKMs) are among the most popular classes of formulas for the approximate numerical integration of nonstiff, initial value problems. However, high-order Runge-Kutta methods require more function evaluations per...

A study of scalar compilation techniques for pipelined supercomputers
Shlomo Weiss, James E. Smith
Pages: 223-245
DOI: 10.1145/79505.79508
This paper studies two compilation techniques for enhancing scalar performance in high-speed scientific processors: software pipelining and loop unrolling. We study the impact of the architecture (size of the register file) and of the hardware...

Efficient formulation of a bivariate nonic C2-hermite polynomial on triangles
Albrecht Preusser
Pages: 246-252
DOI: 10.1145/79505.79509
Bivariate polynomials over triangular domains are widely in use for the definition of surfaces that are continuously differentiable across a set of triangles. A description is given of how explicit formulas...

Algorithm 684: C1- and C2-interplation on triangles with quintic and nonic bivariate polynomials
Albrecht Preusser
Pages: 253-257
DOI: 10.1145/79505.79510

Finding boundaries of the domain of definition for functions along a one-dimensional ray
Orit Shacham, Mordechai Schacham
Pages: 258-268
DOI: 10.1145/79505.79511
A program for finding boundaries of function domains along a one-dimensional ray has been developed. The program decomposes the function into subexpressions which are recursively tested for intervals where they are undefined, negative, or...

An Improved Algorithm for Ordered Sequential Random Sampling
K. Aiyappan Nair
Pages: 269-274
DOI: 10.1145/79505.356313

A dynamic hierarchical subdivision algorithm for computing Delaunay triangulations and other closest-point problems
Oscar Palacios-Velez
Pages: 275-291
DOI: 10.1145/79505.79512
A new, dynamic, hierarchical subdivision and recursive algorithm for computing Delaunay triangulations is presented. The algorithm has four main steps: (1) location of the already formed triangle that contains the point (2) identification of...

ACM Algorithms Policy
Fred T. Krogh
Pages: 293-296
DOI: 10.1145/79505.356315