Least-squares fitting using orthogonal multinomials
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 number of ...
Properly rounded variable precision square root
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 to nearest even in case ...
A note on complex division
An algorithm for computing the quotient of two complex numbers is modified to make it more robust in the presence of underflows.
An efficient derivative-free method for solving nonlinear equations
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 function ...
An evaluation of some new cyclic linear multistep formulas for stiff ODEs
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 evaluated by ...
Solving narrow banded systems on ensemble architectures
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 tridiagonal ...
Equilibrium states of Runge Kutta schemes
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 presented which ...
Inverse pairs of test matrices
Algorithms that are readily programmable are provided for constructing inverse pairs of matrices with elements in a field, a division ring, or a ring.
