About: Derivation of the conjugate gradient method

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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 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.

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rdfs:label	Derivation of the conjugate gradient method (en) 共轭梯度法的推导 (zh)
rdfs:comment	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 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. (en) 在数值线性代数中，共轭梯度法是一种求解对称正定线性方程组的迭代方法。共轭梯度法可以从不同的角度推导而得，包括作为求解最优化问题的的特例，以及作为求解特征值问题的/迭代的变种。本条目记述这些推导方法中的重要步骤。 (zh)
dct:subject	Articles containing proofs Optimization algorithms and methods Numerical linear algebra Gradient methods
Wikipage page ID	26956978 (xsd:integer)
Wikipage revision ID	1077983662 (xsd:integer)
Link from a Wikipage to another Wikipage	Numerical linear algebra Articles containing proofs Conjugate gradient method Orthonormal Symmetric matrix Optimization (mathematics) Eigenvalue Gaussian elimination Arnoldi iteration Krylov subspace Optimization algorithms and methods Iterative method Gram-Schmidt orthogonalization Numerical linear algebra LU factorization Gradient methods Positive-definite matrix System of linear equations Upper Hessenberg matrix Lanczos iteration Partial pivoting dbr:Conjugate_direction_method
Link from a Wikipage to an external page	https://archive.org/details/iterativemethods0000saad%7Curl-access http://nvlpubs.nist.gov/nistpubs/jres/049/6/V49.N06.A08.pdf
sameAs	Derivation of the conjugate gradient method Derivation of the conjugate gradient method Derivation of the conjugate gradient method Derivation of the conjugate gradient method Derivation of the conjugate gradient method
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Cite_journal dbt:Expand_section dbt:Reflist dbt:See dbt:Numerical_linear_algebra
has abstract	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 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. (en) 在数值线性代数中，共轭梯度法是一种求解对称正定线性方程组的迭代方法。共轭梯度法可以从不同的角度推导而得，包括作为求解最优化问题的的特例，以及作为求解特征值问题的/迭代的变种。本条目记述这些推导方法中的重要步骤。 (zh)
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foaf:isPrimaryTopicOf	wikipedia-en:Derivation_of_the_conjugate_gradient_method
is Link from a Wikipage to another Wikipage of	List of numerical analysis topics Gradient method
is foaf:primaryTopic of	wikipedia-en:Derivation_of_the_conjugate_gradient_method

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