About: Generalized minimal residual method

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In mathematics, the generalized minimal residual method (GMRES) is an iterative method for the numerical solution of an indefinite nonsymmetric system of linear equations. The method approximates the solution by the vector in a Krylov subspace with minimal residual. The Arnoldi iteration is used to find this vector.

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rdf:type	software
rdfs:label	Generalized minimal residual method (en)
rdfs:comment	In mathematics, the generalized minimal residual method (GMRES) is an iterative method for the numerical solution of an indefinite nonsymmetric system of linear equations. The method approximates the solution by the vector in a Krylov subspace with minimal residual. The Arnoldi iteration is used to find this vector. (en)
sameAs	Generalized minimal residual method
dbp:wikiPageUsesTemplate	dbt:Doi dbt:ISBN dbt:Numerical_linear_algebra
Subject	Articles with example pseudocode Numerical linear algebra
gold:hypernym	Method
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Generalized_minimal_residual_method?oldid=1073320678&ns=0
Wikipage page ID	4329521 (xsd:integer)
page length (characters) of wiki page	17952 (xsd:nonNegativeInteger)
Wikipage revision ID	1073320678 (xsd:integer)
Link from a Wikipage to another Wikipage	Floating-point arithmetic Normal matrix Numerical analysis Arnoldi iteration Biconjugate gradient method Biconjugate gradient stabilized method Articles with example pseudocode Givens rotation Numerical linear algebra Krylov subspace QR decomposition DIIS Definite matrix Linear independence Linear least squares Preconditioner Triangular matrix Condition number Eigendecomposition of a matrix Eigenvalues and eigenvectors Hessenberg matrix Orthogonal matrix Society for Industrial and Applied Mathematics Sparse matrix Spectrum of a matrix Symmetric matrix System of linear equations Invertible matrix Euclidean space Standard basis Yousef Saad Iterative method Lanczos algorithm Recurrence relation Residual (numerical analysis) dbr:Conjugate_gradient_squared_method dbr:MINRES dbr:Minres dbr:Unsymmetric_Lanczos_iteration
has abstract	In mathematics, the generalized minimal residual method (GMRES) is an iterative method for the numerical solution of an indefinite nonsymmetric system of linear equations. The method approximates the solution by the vector in a Krylov subspace with minimal residual. The Arnoldi iteration is used to find this vector. The GMRES method was developed by Yousef Saad and Martin H. Schultz in 1986. It is a generalization and improvement of the method due to Paige and Saunders in 1975. The MINRES method requires that the matrix is symmetric, but has the advantage that it only requires handling of three vectors. GMRES is a special case of the DIIS method developed by Peter Pulay in 1980. DIIS is applicable to non-linear systems. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Generalized_minimal_residual_method
is Wikipage redirect of	GMRES Gmres Minimal residual method
is Link from a Wikipage to another Wikipage of	Numerical analysis Numerical linear algebra Numerical methods for partial differential equations Anderson acceleration Arnoldi iteration Biconjugate gradient stabilized method Domain decomposition methods Krylov subspace Chebyshev iteration DIIS Lis (linear algebra library) List of numerical analysis topics Computational fluid dynamics Newton–Krylov method Data assimilation Elizabeth Jessup Incomplete LU factorization Mixed finite element method GMRES Factor analysis Iterative method IML++ Gmres Minimal residual method
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Generalized_minimal_residual_method

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