The Lanczos and Conjugate Gradient Algorithms in Finite Precision Arithmetic

• ID: 2359, RIV: 10031993
• ISSN: 0962-4929, ISBN: not specified
• source: Acta Numerica
• keywords: Lanczos; Conjugate; Gradient; Algorithms; Finite; Precision; Arithmetic
• authors: Zdeněk Strakoš
• authors from KNM: Strakoš Zdeněk

Abstract

The Lanczos and conjugate gradient algorithms were introduced more than five decades ago. Because of their fundamental relationship with the theory of orthogonal polynomials and Gauss quadrature of Riemann-Stieltjes integral, they represent very interesting general mathematical objects, with highly nonlinear properties which can be conveniently translated from algebraic language into the language of mathematical analysis, and vice versa. Their numerical behaviour can be explained by an elegant mathematical theory.