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- Stone_method 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 Herbert L. 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 large system of equations, LU decomposition may require a prohibitive amount of memory and number of arithmetical operations.In the preconditioned iterative methods, if the preconditioner matrix M is a good approximation of coefficient matrix A then the convergence is faster. This brings us 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 H. L. 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 equation 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 diagonal for L and three diagonals for U) as the best match of the seven possible equations for the five unknowns for the each row of the matrix.".
- Stone_method wikiPageID "4077966".
- Stone_method wikiPageLength "4154".
- Stone_method wikiPageOutDegree "19".
- Stone_method wikiPageRevisionID "683551280".
- Stone_method wikiPageWikiLink Algorithm.
- Stone_method wikiPageWikiLink Category:Articles_with_example_pseudocode.
- Stone_method wikiPageWikiLink Category:Numerical_linear_algebra.
- Stone_method wikiPageWikiLink Elliptic_operator.
- Stone_method wikiPageWikiLink Finite_difference.
- Stone_method wikiPageWikiLink Incomplete_LU_factorization.
- Stone_method wikiPageWikiLink Instruction_set.
- Stone_method wikiPageWikiLink Iterative_method.
- Stone_method wikiPageWikiLink Joel_H._Ferziger.
- Stone_method wikiPageWikiLink LU_decomposition.
- Stone_method wikiPageWikiLink Numerical_analysis.
- Stone_method wikiPageWikiLink Partial_differential_equation.
- Stone_method wikiPageWikiLink Pentadiagonal_matrix.
- Stone_method wikiPageWikiLink Preconditioner.
- Stone_method wikiPageWikiLink Random-access_memory.
- Stone_method wikiPageWikiLink Sparse_matrix.
- Stone_method wikiPageWikiLink System_of_linear_equations.
- Stone_method wikiPageWikiLink Two-dimensional_space.
- Stone_method wikiPageWikiLinkText "Stone method".
- Stone_method wikiPageWikiLinkText "Stone's method".
- Stone_method wikiPageUsesTemplate Template:!.
- Stone_method wikiPageUsesTemplate Template:=.
- Stone_method wikiPageUsesTemplate Template:CFDWiki.
- Stone_method wikiPageUsesTemplate Template:Cite_book.
- Stone_method wikiPageUsesTemplate Template:Cite_journal.
- Stone_method wikiPageUsesTemplate Template:Math.
- Stone_method wikiPageUsesTemplate Template:No_footnotes.
- Stone_method wikiPageUsesTemplate Template:Numerical_linear_algebra.
- Stone_method wikiPageUsesTemplate Template:Primary_sources.
- Stone_method subject Category:Articles_with_example_pseudocode.
- Stone_method subject Category:Numerical_linear_algebra.
- Stone_method hypernym Algorithm.
- Stone_method type Software.
- Stone_method 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 Herbert L. Stone, who proposed it in 1968.The LU decomposition is an excellent general purpose linear equation solver.".
- Stone_method label "Stone method".
- Stone_method sameAs Q7619072.
- Stone_method sameAs m.0bgyl9.
- Stone_method sameAs Q7619072.
- Stone_method wasDerivedFrom Stone_method?oldid=683551280.
- Stone_method isPrimaryTopicOf Stone_method.