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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 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".
- Crout_matrix_decomposition wikiPageExternalLink matlab-crout-lu-factorization-linear-equations-systems.php.
- Crout_matrix_decomposition wikiPageID "900131".
- Crout_matrix_decomposition wikiPageRevisionID "604547889".
- Crout_matrix_decomposition hasPhotoCollection Crout_matrix_decomposition.
- Crout_matrix_decomposition subject Category:Matrix_decompositions.
- Crout_matrix_decomposition type Abstraction100002137.
- Crout_matrix_decomposition type Algebra106012726.
- Crout_matrix_decomposition type Cognition100023271.
- Crout_matrix_decomposition type Content105809192.
- Crout_matrix_decomposition type Decomposition106013471.
- Crout_matrix_decomposition type Discipline105996646.
- Crout_matrix_decomposition type KnowledgeDomain105999266.
- Crout_matrix_decomposition type Mathematics106000644.
- Crout_matrix_decomposition type MatrixDecompositions.
- Crout_matrix_decomposition type PsychologicalFeature100023100.
- Crout_matrix_decomposition type PureMathematics106003682.
- Crout_matrix_decomposition type Science105999797.
- Crout_matrix_decomposition type VectorAlgebra106013298.
- 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 Crout. The Crout matrix decomposition algorithm differs slightly from the Doolittle method.".
- Crout_matrix_decomposition label "Crout matrix decomposition".
- Crout_matrix_decomposition label "Crout-decompositie".
- 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 sameAs Crout_matrix_decomposition.
- Crout_matrix_decomposition wasDerivedFrom Crout_matrix_decomposition?oldid=604547889.
- Crout_matrix_decomposition isPrimaryTopicOf Crout_matrix_decomposition.