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ABS algorithms for linear equations and ABSPACK. (English) Zbl 0985.65022
The basic properties of the scaled Abaffy-Broden-Spadicato (ABS) algorithms intended to solve linear equations and applied to linear least squares, nonlinear equations and optimization problems are discussed. The derivation of ABS methods for linear Diophantine equations is presented and several ABS algorithms for solving different type of equations are described in details. The ABSPACK package for solving linear and nonlinear systems of equations and optimization problems using the ABS algorithms is described and a comparison is given with some LAPACK and LINPACK codes.

MSC:
65F10 Iterative numerical methods for linear systems
11D04 Linear Diophantine equations
65Y15 Packaged methods for numerical algorithms
65H10 Numerical computation of solutions to systems of equations
65K05 Numerical mathematical programming methods
65F35 Numerical computation of matrix norms, conditioning, scaling
Software:
ABSPACK; LAPACK; LINPACK
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