About: Conjugate gradient method

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Conjugate gradient method Goto Sponge NotDistinct Permalink

An Entity of Type : dbo:Software, within Data Space : el.dbpedia.org associated with source document(s)

In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the Cholesky decomposition. Large sparse systems often arise when numerically solving partial differential equations or optimization problems.

Attributes	Values
rdf:type	Thing software
rdfs:label	Conjugate gradient method (en)
rdfs:comment	In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the Cholesky decomposition. Large sparse systems often arise when numerically solving partial differential equations or optimization problems. (en)
rdfs:seeAlso	Preconditioner
sameAs	Conjugate gradient method Conjugate gradient method
dbp:wikiPageUsesTemplate	dbt:= dbt:Authority_control dbt:Cite_book dbt:Div_col dbt:Div_col_end dbt:Main dbt:Math dbt:Mvar dbt:Reflist dbt:See_also dbt:Short_description dbt:Springer dbt:Numerical_linear_algebra
Subject	Articles with example MATLAB/Octave code Numerical linear algebra Gradient methods
Link from a Wikipage to an external page	https://archive.org/details/iterativemethods0000saad https://archive.org/details/introductiontonu0000atki https://archive.org/details/iterativemethods0000saad%7Cchapter-url-access=registration%7Cedition=2nd%7Cchapter=Chapter https://web.stanford.edu/group/SOL/software/lsqr/
thumbnail	wiki-commons:Special:FilePath/Conjugate_gradient_illustration.svg?width=300
foaf:depiction
gold:hypernym	Algorithm
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Conjugate_gradient_method?oldid=1071210601&ns=0
Wikipage page ID	1448821 (xsd:integer)
page length (characters) of wiki page	40066 (xsd:nonNegativeInteger)
Wikipage revision ID	1071210601 (xsd:integer)
Link from a Wikipage to another Wikipage	List of things named after Charles Hermite Magnus Hestenes Nonlinear conjugate gradient method Numerical analysis Round-off error Algorithm Anne Greenbaum Arnoldi iteration Basis (linear algebra) Belief propagation Biconjugate gradient method Articles with example MATLAB/Octave code Jacobi method Numerical linear algebra Double-precision floating-point format Double integrator Krylov subspace Quadratic function Cholesky decomposition Definite matrix Line search Linear least squares Preconditioner Condition number Conjugate gradient method Conjugate residual method Conjugate transpose Eduard Stiefel Eigenvalues and eigenvectors Hessian matrix Optimal control Partial differential equation Sparse matrix Sparse matrix-vector multiplication Spectrum of a matrix Energy minimization GNU Octave Gauss–Seidel method Gradient descent Gram–Schmidt process Incomplete Cholesky factorization Symmetric matrix System of linear equations Feedback Inner product space Transpose Z4 (computer) Iterative method Lanczos algorithm MATLAB Mathematical optimization Mathematics Polynomial ring Real number Residual (numerical analysis) Gradient methods
has abstract	In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the Cholesky decomposition. Large sparse systems often arise when numerically solving partial differential equations or optimization problems. The conjugate gradient method can also be used to solve unconstrained optimization problems such as energy minimization. It is commonly attributed to Magnus Hestenes and Eduard Stiefel, who programmed it on the Z4, and extensively researched. The biconjugate gradient method provides a generalization to non-symmetric matrices. Various nonlinear conjugate gradient methods seek minima of nonlinear optimization problems. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Conjugate_gradient_method
is Wikipage redirect of	Preconditioned conjugate gradient method Conjugate Gradient method CG method Conjugate Gradient Squared Conjugate gradient Conjugate gradient algorithm Conjugate gradient descent

Faceted Search & Find service v1.17_git151 as of Feb 20 2025

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Nov 11 2024, on Linux (x86_64-ubuntu_focal-linux-gnu), Single-Server Edition (72 GB total memory, 1 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2025 OpenLink Software