Spedicato, E.; Xia, Z.; Bodon, E.; Del Popolo, A. ABS algorithms for linear equations and ABSPACK. (English) Zbl 0985.65022 Ann. Univ. Ferrara, Nuova Ser., Sez. VII 46, Suppl., 611-629 (2000). 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. Reviewer: Petko Hr.Petkov (Sofia) Cited in 8 Documents 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 Keywords:scaling; Abaffy-Broyden-Spadicato algorithms; linear least squares; nonlinear equations; optimization; ABS methods; Diophantine equations; ABSPACK package; comparison; LAPACK; LINPACK Software:LAPACK; LINPACK; ABSPACK PDFBibTeX XMLCite \textit{E. Spedicato} et al., Ann. Univ. Ferrara, Nuova Ser., Sez. VII 46, 611--629 (2000; Zbl 0985.65022) Full Text: arXiv