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In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as where and .

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rdfs:label	Tridiagonal matrix algorithm (en)
rdfs:comment	In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as where and . (en)
sameAs	Tridiagonal matrix algorithm
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Reflist dbt:Wikibooks dbt:Numerical_linear_algebra dbt:CFDWiki
Subject	Articles with example BASIC code Numerical linear algebra
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm?oldid=1056852364&ns=0
Wikipage page ID	4068264 (xsd:integer)
page length (characters) of wiki page	10787 (xsd:nonNegativeInteger)
Wikipage revision ID	1056852364 (xsd:integer)
has abstract	In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as where and . For such systems, the solution can be obtained in operations instead of required by Gaussian elimination. A first sweep eliminates the 's, and then an (abbreviated) backward substitution produces the solution. Examples of such matrices commonly arise from the discretization of 1D Poisson equation and natural cubic spline interpolation. Thomas' algorithm is not stable in general, but is so in several special cases, such as when the matrix is diagonally dominant (either by rows or columns) or symmetric positive definite; for a more precise characterization of stability of Thomas' algorithm, see Higham Theorem 9.12. If stability is required in the general case, Gaussian elimination with partial pivoting (GEPP) is recommended instead. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm
is Wikipage redirect of	Tridiagonal matrix algorithm/Derivation Thomas algorithm
is Link from a Wikipage to another Wikipage of	Llewellyn Thomas Alternating-direction implicit method Beam and Warming scheme Block matrix Discrete Poisson equation List of numerical analysis topics Computational methods for free surface flow Crank–Nicolson method EAS3 List of algorithms
is known for of	Llewellyn Thomas

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