Methods of conjugate gradients for solving linear systems

Magnus R. Hestenes; Eduard Stiefel · Journal of research of the National Bureau of Standards · 1952

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Author / responsible party

Magnus R. Hestenes; Eduard Stiefel

Publisher

Journal of research of the National Bureau of Standards

Year

1952

Language

English

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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.

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APA 7

Hestenes, M. R. & Stiefel, E. (1952). Methods of conjugate gradients for solving linear systems. https://doi.org/10.6028/jres.049.044

MLA

Hestenes, Magnus R, and Eduard Stiefel. "Methods of conjugate gradients for solving linear systems." 1952. https://doi.org/10.6028/jres.049.044.

Chicago

Hestenes, Magnus R. and Eduard Stiefel. 1952. "Methods of conjugate gradients for solving linear systems.". https://doi.org/10.6028/jres.049.044.

Harvard

Hestenes, M. R. and Stiefel, E. 1952, Methods of conjugate gradients for solving linear systems, Journal of research of the National Bureau of Standards, available at: https://doi.org/10.6028/jres.049.044 [Accessed 6 Aug. 2026].

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Title: Methods of conjugate gradients for solving linear systems

Author / contributors: Magnus R. Hestenes; Eduard Stiefel

Publisher: Journal of research of the National Bureau of Standards

Publication year: 1952

Language: English

Subjects

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Conjugate; Conjugate gradient method; Computer science; Mathematics; Applied mathematics; Mathematical analysis; Algorithm