publication . Other literature type . Article . 1952

Methods of conjugate gradients for solving linear systems

Eduard Stiefel; Magnus R. Hestenes;

Open Access

Published: 01 Dec 1952

Publisher: National Institute of Standards and Technology (NIST)

Summary

Abstract

An iterative algorithm is given for solving a system Ax=k of n linear equations in n unknowns. The solution is given in n steps. It is shown that this method is a special case of a very general method which also includes Gaussian elimination. These general algorithms are essentially algorithms for finding an n dimensional ellipsoid. Connections are made with the theory of orthogonal polynomials and continued fractions.

doi: 10.6028/jres.049.044

Subjects

free text keywords: Biconjugate gradient method, Conjugate residual method, Iterative method, Linear system, Applied mathematics, Orthogonal polynomials, Derivation of the conjugate gradient method, Conjugate gradient method, Gaussian elimination, symbols.namesake, symbols, Mathematics

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