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Methods of conjugate gradients for solving linear systems

1952; US government; Volume: 49; Issue: 6 Linguagem: Inglês

10.6028/jres.049.044

2376-5305

Magnus R. Hestenes, Eduard Stiefel,

Statistical and numerical algorithms

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.