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- Crout_matrix_decomposition abstract "In linear algebra, the Crout matrix decomposition is an LU decomposition which decomposes a matrix into a lower triangular matrix (L), an upper triangular matrix (U) and, although not always needed, a permutation matrix (P). It was developed by Prescott Durand Crout. The Crout matrix decomposition algorithm differs slightly from the Doolittle method. Doolittle's method returns a unit lower triangular matrix and an upper triangular matrix, while the Crout method returns a lower triangular matrix and a unit upper triangular matrix.So, if a matrix decomposition of a matrix A is such that:A = LDUbeing L a unit lower triangular matrix, D a diagonal matrix and U a unit upper triangular matrix, then Doolittle's method producesA = L(DU)and Crout's method producesA = (LD)U.being L a lower triangular matrix, D a diagonal matrix and U a normalised upper triangular matrixC implementation:Octave/Matlab implementation: function [L, U] = LUdecompCrout(A) [R, C] = size(A); for i = 1:R L(i, 1) = A(i, 1); U(i, i) = 1; end for j = 2:R U(1, j) = A(1, j) / L(1, 1); end for i = 2:R for j = 2:i L(i, j) = A(i, j) - L(i, 1:j - 1) * U(1:j - 1, j); end for j = i + 1:R U(i, j) = (A(i, j) - L(i, 1:i - 1) * U(1:i - 1, j)) / L(i, i); end end end".
- Crout_matrix_decomposition wikiPageExternalLink matlab-crout-lu-factorization-linear-equations-systems.php.
- Crout_matrix_decomposition wikiPageID "900131".
- Crout_matrix_decomposition wikiPageLength "2597".
- Crout_matrix_decomposition wikiPageOutDegree "10".
- Crout_matrix_decomposition wikiPageRevisionID "671835484".
- Crout_matrix_decomposition wikiPageWikiLink Algorithm.
- Crout_matrix_decomposition wikiPageWikiLink Category:Matrix_decompositions.
- Crout_matrix_decomposition wikiPageWikiLink Doolittle_decomposition.
- Crout_matrix_decomposition wikiPageWikiLink LU_decomposition.
- Crout_matrix_decomposition wikiPageWikiLink Linear_algebra.
- Crout_matrix_decomposition wikiPageWikiLink Lower_triangular_matrix.
- Crout_matrix_decomposition wikiPageWikiLink Matrix_(mathematics).
- Crout_matrix_decomposition wikiPageWikiLink Permutation_matrix.
- Crout_matrix_decomposition wikiPageWikiLink Prescott_Durand_Crout.
- Crout_matrix_decomposition wikiPageWikiLink Triangular_matrix.
- Crout_matrix_decomposition wikiPageWikiLink Upper_triangular_matrix.
- Crout_matrix_decomposition wikiPageWikiLinkText "Crout matrix decomposition".
- Crout_matrix_decomposition hasPhotoCollection Crout_matrix_decomposition.
- Crout_matrix_decomposition wikiPageUsesTemplate Template:Reflist.
- Crout_matrix_decomposition subject Category:Matrix_decompositions.
- Crout_matrix_decomposition hypernym Decomposition.
- Crout_matrix_decomposition type Article.
- Crout_matrix_decomposition type Article.
- Crout_matrix_decomposition type Decomposition.
- Crout_matrix_decomposition comment "In linear algebra, the Crout matrix decomposition is an LU decomposition which decomposes a matrix into a lower triangular matrix (L), an upper triangular matrix (U) and, although not always needed, a permutation matrix (P). It was developed by Prescott Durand Crout. The Crout matrix decomposition algorithm differs slightly from the Doolittle method.".
- Crout_matrix_decomposition label "Crout matrix decomposition".
- Crout_matrix_decomposition sameAs Crout-algoritmus.
- Crout_matrix_decomposition sameAs Crout-decompositie.
- Crout_matrix_decomposition sameAs m.03n33z.
- Crout_matrix_decomposition sameAs Q15924432.
- Crout_matrix_decomposition sameAs Q15924432.
- Crout_matrix_decomposition wasDerivedFrom Crout_matrix_decomposition?oldid=671835484.
- Crout_matrix_decomposition isPrimaryTopicOf Crout_matrix_decomposition.