**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