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LU decomposition on MathWorld. LU decomposition on Math-Linux. LU decomposition at Holistic Numerical Methods Institute; LU matrix factorization. MATLAB reference. Computer code. LAPACK is a collection of FORTRAN subroutines for solving dense linear algebra problems; ALGLIB includes a partial port of the LAPACK to C++, C#, Delphi, etc.
In linear algebra, a Block LU decomposition is a matrix decomposition of a block matrix into a lower block triangular matrix L and an upper block triangular matrix U. This decomposition is used in numerical analysis to reduce the complexity of the block matrix formula.
is called an incomplete LU decomposition (with respect to the sparsity pattern ). The sparsity pattern of L and U is often chosen to be the same as the sparsity pattern of the original matrix A . If the underlying matrix structure can be referenced by pointers instead of copied, the only extra memory required is for the entries of L and U .
When P is an identity matrix, the LUP decomposition reduces to the LU decomposition. Comments: The LUP and LU decompositions are useful in solving an n-by-n system of linear equations =. These decompositions summarize the process of Gaussian elimination in matrix form.
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. [1] The Crout matrix decomposition algorithm differs slightly from the ...
A frontal solver builds a LU or Cholesky decomposition of a sparse matrix. Frontal solvers start with one or a few diagonal entries of the matrix, then consider all of those diagonal entries that are coupled to the first set via off-diagonal entries, and so on.
The Doolittle algorithm for LU decomposition in numerical analysis and linear algebra; The most common method of rearing queen bees This page was last edited on 18 ...
Common problems in numerical linear algebra include obtaining matrix decompositions like the singular value decomposition, the QR factorization, the LU factorization, or the eigendecomposition, which can then be used to answer common linear algebraic problems like solving linear systems of equations, locating eigenvalues, or least squares ...