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.
Keywords
ConjugateConjugate gradient methodComputer scienceMathematicsApplied mathematicsMathematical analysisAlgorithm
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Publication Info
- Year
- 1952
- Type
- article
- Volume
- 49
- Issue
- 6
- Pages
- 409-409
- Citations
- 7835
- Access
- Closed
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Cite This
Magnus R. Hestenes,
Eduard Stiefel
(1952).
Methods of conjugate gradients for solving linear systems.
Journal of research of the National Bureau of Standards
, 49
(6)
, 409-409.
https://doi.org/10.6028/jres.049.044
Identifiers
- DOI
- 10.6028/jres.049.044