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In numerical analysis, Stone's method, also known as the strongly implicit procedure or SIP, is an algorithm for solving a sparse linear system of equations. The method uses an incomplete LU decomposition, which approximates the exact LU decomposition, to get an iterative solution of the problem. The method is named after Harold S. Stone, who proposed it in 1968. In the iterative methods, if the preconditioner matrix M is a good approximation of coefficient matrix A then the convergence is faster. This brings one to idea of using approximate factorization LU of A as the iteration matrix M.

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rdfs:label	Stone's method (en)
rdfs:comment	In numerical analysis, Stone's method, also known as the strongly implicit procedure or SIP, is an algorithm for solving a sparse linear system of equations. The method uses an incomplete LU decomposition, which approximates the exact LU decomposition, to get an iterative solution of the problem. The method is named after Harold S. Stone, who proposed it in 1968. In the iterative methods, if the preconditioner matrix M is a good approximation of coefficient matrix A then the convergence is faster. This brings one to idea of using approximate factorization LU of A as the iteration matrix M. (en)
dcterms:subject	Articles with example pseudocode Numerical linear algebra
Wikipage page ID	4077966 (xsd:integer)
Wikipage revision ID	1100842518 (xsd:integer)
Link from a Wikipage to another Wikipage	Algorithm Incomplete LU factorization Pentadiagonal matrix Elliptic operator LU decomposition Articles with example pseudocode Joel H. Ferziger Finite difference Numerical analysis Partial differential equation Iterative method Harold S. Stone Numerical linear algebra Sparse matrix Instruction (computer science) Linear system of equations Random access memory Two-dimensional dbr:Preconditioned
sameAs	Stone's method Stone's method
dbp:wikiPageUsesTemplate	dbt:! dbt:= dbt:Cite_book dbt:Cite_journal dbt:Clarify dbt:Math dbt:Multiple_issues dbt:No_footnotes dbt:Primary_sources dbt:Reflist dbt:Numerical_linear_algebra dbt:CFDWiki
date	March 2016 (en)
reason	vague (en)
has abstract	In numerical analysis, Stone's method, also known as the strongly implicit procedure or SIP, is an algorithm for solving a sparse linear system of equations. The method uses an incomplete LU decomposition, which approximates the exact LU decomposition, to get an iterative solution of the problem. The method is named after Harold S. Stone, who proposed it in 1968. The LU decomposition is an excellent general-purpose linear equation solver. The biggest disadvantage is that it fails to take advantage of coefficient matrix to be a sparse matrix. The LU decomposition of a sparse matrix is usually not sparse, thus, for a large system of equations, LU decomposition may require a prohibitive amount of memory and number of arithmetical operations. In the iterative methods, if the preconditioner matrix M is a good approximation of coefficient matrix A then the convergence is faster. This brings one to idea of using approximate factorization LU of A as the iteration matrix M. A version of incomplete lower-upper decomposition method was proposed by Stone in 1968. This method is designed for equation system arising from discretisation of partial differential equations and was firstly used for a pentadiagonal system of equations obtained while solving an elliptic partial differential equation in a two-dimensional space by a finite difference method. The LU approximate decomposition was looked in the same pentadiagonal form as the original matrix (three diagonals for L and three diagonals for U) as the best match of the seven possible equations for the five unknowns for each row of the matrix. (en)
prov:wasDerivedFrom	wikipedia-en:Stone's_method?oldid=1100842518&ns=0
page length (characters) of wiki page	4274 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Stone's_method
is Link from a Wikipage to another Wikipage of	List of algorithms List of numerical analysis topics Stone method Strongly implicit procedure
is Wikipage redirect of	Stone method Strongly implicit procedure
is foaf:primaryTopic of	wikipedia-en:Stone's_method

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