Stanley Cabay

Congruence Techniques for the Exact Solution of Integer Systems of Linear Equations

A new Fortran code, ESOLVE, is discussed for the exact solution of systems of linear equations with multiple-precision integer coefficients by congruence techniques. The code runs significantly faster than other codes which use congruential techniques. Test runs on two classes of problems reveal that the congruential method is competitive with the two-step multipleprecision method for solving integer systems exactly.

Algebraic computations of scaled pade´ fractions

Two companion algorithms are developed for constructing Pade fractions along an off-diagonal path of the Pade table for a function

Matrix Pade´ fractions and their computation

{{ - A(z)} / {B(z)}}

Fraction-free computation of matrix Padé systems

, where

Algorithm 522: ESOLVE, Congruence Techniques for the Exact Solution of Integer Systems of Linear Equations [F4]

A(z)

A superfast algorithm for multi-dimensional Padé systems

and

Power series remainder sequences and Padé fractions over an integral domain

B(z)

Systems of linear equations with dense univariate polynomial coefficients

are formal power series over a field.One of the algorithms computes the first n Pade fractions along the off-diagonal in time

Algorithm 766: experiments with a weakly stable algorithm for computing Padé-Hermite and simultaneous Padé approximants

O(n^2 )

A fast, reliable algorithm for calculating Pade´-Hermite forms

. When