Mathematical Software (TOMS)


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ACM Transactions on Mathematical Software (TOMS), Volume 11 Issue 3, Sept. 1985

Least-squares fitting using orthogonal multinomials
Richard H. Bartels, John J. Jezioranski
Pages: 201-217
DOI: 10.1145/214408.214410
Forsythe has given a method for generating basis polynomials in a single variable that are orthogonal with respect to a given inner product. Weisfeld later demonstrated that Forsythe's approach could be extended to polynomials in an arbitrary...

Algorithm 634: CONSTR and EVAL: routines for fitting multinomials in a least-squares sense
Richard H. Bartels, John J. Jezioranski
Pages: 218-228
DOI: 10.1145/214408.214412

Properly rounded variable precision square root
T. E. Hull, A. Abrham
Pages: 229-237
DOI: 10.1145/214408.214413
The square root function presented here returns a properly rounded approximation to the square root of its argument, or it raises an error condition if the argument is negative. Properly rounded means rounded to the nearest, or...

A note on complex division
G. W. Stewart
Pages: 238-241
DOI: 10.1145/214408.214414
An algorithm for computing the quotient of two complex numbers is modified to make it more robust in the presence of underflows.

ALGORITHM 635: an algorithm for the solution of systems of complex linear equations in the L norm with constraints on the unknowns
Roy L. Streit
Pages: 242-249
DOI: 10.1145/214408.214415

An efficient derivative-free method for solving nonlinear equations
D. Le
Pages: 250-262
DOI: 10.1145/214408.214416
An algorithm is presented for finding a root of a real function. The algorithm combines bisection with second and third order methods using derivatives estimated from objective function values. Globaql convergence is ensured and the number of...

An evaluation of some new cyclic linear multistep formulas for stiff ODEs
P. E. Tischer, G. K. Gupta
Pages: 263-270
DOI: 10.1145/214408.214417
We evaluate several sets of cyclic linear multistep formulas (CLMFs). One of these sets was derived by Tischer and Sacks-Davis. Three new sets of formulas have been derived and we present their characteristics.The formulas have been...

Solving narrow banded systems on ensemble architectures
S. Lennart Johnsson
Pages: 271-288
DOI: 10.1145/214408.214418
We present concurrent algorithms for the solution of narrow banded systems on ensemble architectures, and analyze the communication and arithmetic complexities of the algorithms. The algorithms consist of three phases. In phase 1, a block...

Equilibrium states of Runge Kutta schemes
George Hall
Pages: 289-301
DOI: 10.1145/214408.214424
Understanding the behavior of Runge-Kutta codes when stability considerations restrict the stepsize provides useful information for stiffness detection and other implementation details. Analysis of equilibrium states on test problems is...

Inverse pairs of test matrices
Wilhelm S. Ericksen
Pages: 302-304
DOI: 10.1145/214408.214425
Algorithms that are readily programmable are provided for constructing inverse pairs of matrices with elements in a field, a division ring, or a ring.

Remark on algorithm 620
Dennis E. Hamilton
Pages: 305-307
DOI: 10.1145/214408.214426