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Derivation of the conjugate gradient method : ウィキペディア英語版 | Derivation of the conjugate gradient method In numerical linear algebra, the conjugate gradient method is an iterative method for numerically solving the linear system : where is symmetric positive-definite. The conjugate gradient method can be derived from several different perspectives, including specialization of the conjugate direction method for optimization, and variation of the Arnoldi/Lanczos iteration for eigenvalue problems. The intent of this article is to document the important steps in these derivations. ==Derivation from the conjugate direction method==
The conjugate gradient method can be seen as a special case of the conjugate direction method applied to minimization of the quadratic function :
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