
	Where results make sense

Topic: Crout decomposition

Related Topics

Lower triangular matrix

LU decomposition

Block LU decomposition

Matrix decomposition

Cholesky decomposition

Identity matrix

Manny Shinwell

Glasgow Subway

2004

Alfred Nobel

Strathclyde Passenger Transport

Upper triangular matrix

LU factorization

	LU decomposition - Wikipedia, the free encyclopedia
		In linear algebra, the LU decomposition is a matrix decomposition which writes a matrix as the product of a lower and upper triangular matrix.
		This decomposition is used in numerical analysis to solve systems of linear equations.
		The Crout algorithm is slightly different and constructs a lower triangular matrix and an unit upper triangular matrix.
	en.wikipedia.org /wiki/LU_decomposition (704 words)

	Direct Methods
		The decomposition of the matrix and solution of the system (2.28) is, however, a process of the order of magnitude
		Math92], which roughly means that if you double the number of rows and columns of the matrix, the number of arithmetic operations that must be performed increases by a factor of 8.
		That is one major problem with the application of the LU decomposition, and even with large systems of sparse matrices the number of operations increases superlinearly with a growing matrix dimension.
	www.exp-math.uni-essen.de /~ajung/diplom/node15.html (267 words)

	FDLIB Directories (Site not responding. Last check: 2007-10-25)
		Cholesky decomposition of a symmetric and positive-definite matrix by column or row.
		decomposition, computation of the determinant and inverse of a matrix.
		Decomposition of a time series into normal modes expressing exponentially growing or decaying sinusoidal waves.
	stokes.ucsd.edu /c_pozrikidis/FDLIB/mdc.html (5443 words)

	Templateding_math::MatrixLuDecomposer< TValue > class Reference
		Fetches the L part from the decomposition to a given matrix.
		Permutates a given matrix according to the permutation vector from this decomposition.
		The number of rows of the given matrix must be equal to that of the source matrix, and the decomposition has been done successfully.
	mywebpages.comcast.net /ylding/c/ding/classding__math_1_1MatrixLuDecomposer.html (705 words)

	LUDecompositionQuick (Colt 1.2.0 - API Specification)
		Usage pattern is as follows: Create an instance of this class, call a decompose method, then retrieve the decompositions, determinant, and/or solve as many equation problems as needed.
		The LU decomposition with pivoting always exists, even if the matrix is singular, so the decompose methods will never fail.
		The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations.
	dsd.lbl.gov /~hoschek/colt/api/cern/colt/matrix/linalg/LUDecompositionQuick.html (419 words)

	LU decomposition
		LU decomposition, or Doolittle decomposition is the process of decomposing a matrix into a product of an upper-triangular matrix U and a lower triangular matrix L.
		LU decomposition is LUP decomposition[?], where P is the identity matrix.
		The text of this article is licensed under the GFDL.
	www.ebroadcast.com.au /lookup/encyclopedia/lu/LU_decomposition.html (244 words)

	TDecompLU
		LU Decomposition class Decompose a general n x n matrix A into P A = L U where P is a permutation matrix, L is unit lower triangular and U is upper triangular.
		The decomposition fails if a diagonal element of abs(fLU) is == 0, The matrix fUL is made invalid.
		The decomposition is stored in fLU: U is explicit in the upper triag and L is in multiplier form in the subdiagionals.
	root.cern.ch /root/html/TDecompLU.html (537 words)

	Homework 10 (Site not responding. Last check: 2007-10-25)
		Find the Crout's method of LU decomposition by hand.
		(10 points) Modify the LU Decomposition program to do a Crout decomposition of a matrix.
		The program from class does the Doolittle decomposition.
	stommel.tamu.edu /~esandt/Teach/Summer02/CVEN302/Homework/Assign10/HW10.html (151 words)

	Up ..Up.. and Away.. (Site not responding. Last check: 2007-10-25)
		He proved that O(N5/2) comparisons and additions are sufficient to compute the shortest distance between all N(N-1) pairs of vertices in a directed graph with nonnegative edge weights.
		In 1976, Goto, Ohtsuki and Yoshimura used Carre's formulation of the shortest path problem and gave an algorithm based on Crout decomposition of linear algebra.
		The implementation methods presented in this paper are powerful when a network of fixed sparseness structure must be solves repeatedly with different numerical values of arc lengths.
	www.me.utexas.edu /~jensen/ORMM/classes/units/networks/topic_pages/Bhaskaran/page5.html (333 words)

	DRA Systems: OR-Objects 1.2.4: Package drasys.or.linear.algebra
		The interface used by all algorithms to access LU decomposition algorithms.
		An implementation of LU decomposition using Crout's algorithm with partial pivoting.
		A singular value decomposition implementation using QR iteration.
	opsresearch.com /OR-Objects/api/drasys/or/linear/algebra/package-summary.html (52 words)

	Lecture 13 (Site not responding. Last check: 2007-10-25)
		This link is the powerpoint presentation put together for class on LU decomposition.
		LU_crout_factor - matlab program is a program, which does the Crout's LU decomposition of a matrix and results in a L and U matrix.
		LU_Solve - matlab program is a program, which uses the LU decomposition to solve a set of values.
	stommel.tamu.edu /~esandt/Teach/Fall01/CVEN302/Lectures/Lecture13/layout13.html (78 words)

	Solving linear equation systems
		LU decomposition (decomposition into a lower and upper triangular matrix) is recommended when dealing with equation systems where the matrix A does not alter but the right hand side (the vector z) does.
		The decomposition of the matrix A into a lower and upper triangular matrix is not unique.
		The most important decompositions, based on Gaussian elimination, are the Doolittle, the Crout and the Cholesky decomposition.
	qucs.sourceforge.net /tech/node16.html (1620 words)

	The Algorithm
		That is, a new LU decomposition is not needed.
		When using either Crout's or Doolittle's definition of the LU decomposition during the AC analysis the decomposition representation changes during the AC noise analysis as the matrix
		Thus the forward substitution (as described in section 3.2.4) and the backward substitution (as described in section 3.2.4) must be slightly modified.
	qucs.sourceforge.net /tech/node24.html (659 words)

	[No title]
		For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U. If m
		The LU decompostion with pivoting always exists, even if the matrix is singular, so the constructor will never fail.
		In Java, we suspect the dot-product, Crout algorithm will be faster.
	astro.u-strasbg.fr /~fmurtagh/mda-sw/MDAJ/src/LUDecomposition.java (408 words)

	1.5 Correspondence: operator-module
		For the particular case of the domain decomposition method, all the above operators are used, as this algorithm performs iterations on the unknowns on the sub-domain interfaces, the unknowns inside the sub-domains being recomputed at each iteration by a direct method.
		ICHRGC conjugate gradient iterations preconditioned by incomplete factorization of Cholesky or Crout, for positive definite symmetric matrices (structure AMAT in main memory)
		For the case of a domain decomposition method, we need to use specific operators (super modules that use the preceding algorithms):
	www-rocq.inria.fr /modulef/Doc/GB/Guide5-14/node10.html (551 words)

	KPG1_LUDCx - Performs an LU decomposition of a square matrix
		This routine performs a decomposition of a square matrix into lower and upper triangular matrices using Crout
		An index of the row permutations caused by the partial pivoting.
		If EVEN is.TRUE., there was an even number of row interchanges during the decomposition.
	star-www.rl.ac.uk /star/docs/sun238.htx/node488.html (284 words)

	Matrix Operations (Site not responding. Last check: 2007-10-25)
		Decomposes matrixes using Crout's method with partial pivoting.
		The lu-matrix argument holds the result of the decomposition.
		An integer-array that is filled to record the row permutation produced by partial pivoting.
	www.cs.fsu.edu /g2/g2doc/g2sprm/matrix16.htm (31 words)

	1.6. LU decomposition (Site not responding. Last check: 2007-10-25)
		is again an LU decomposition, if D is a diagonal matrix.
		The construction of an LU decomposition can be done by the Crout's algorithm, for example.
		Usually we construct an LU decomposition by means of the Gaussian elimination in such a way that L is formed from the coefficients used in the elimination while U is the matrix A itself after the elimination.
	www.ee.oulu.fi /~mpa/matreng/ematr1_6.htm (146 words)

	Cholesky, Doolittle and Crout Factorization
		If L has 1's on it's diagonal, then it is called a Doolittle factorization.
		If U has 1's on its diagonal, then it is called a Crout factorization.
		For curiosity, the reader might be interested in other methods of computing L and U.
	math.fullerton.edu /mathews/n2003/CholeskyMod.html (339 words)

	Constrained, non-linear, derivative-free parallel optimization of continuous, high computing load, noisy objective ... (Site not responding. Last check: 2007-10-25)
		The Cholesky decomposition can be applied on any square matrix
		The Cholesky decomposition is one of the fastest decomposition available.
		The Cholesky decomposition is a particular case of the
	iridia.ulb.ac.be /~fvandenb/work/thesis/node72.html (332 words)

	[No title]
		Write the equations in the matrix form: EMBED Equation b.
		Use Crout decomposition to transform the matrix of coefficients into the product of a lower triangular matrix and an upper triangular matrix (1’s on the diagonal) in the form: EMBED Equation .
		Multiply the lower and upper matrices to show that the original coefficient matrix is obtained.
	www.engr.udayton.edu /faculty/fbogner/cie320/h11.doc (135 words)

	ASU PHY 502 - Lecture 9 (Site not responding. Last check: 2007-10-25)
		In fact, there is additional freedom in this breakup, so we can set the diagonal of the lower matrix to be all ones.
		These decompositions can be done in place, which saves on memory useage.
		By solving the equations in a particular order (Crout's algorithm), they are easily solved.
	phy.asu.edu /phy502-shumway/notes/lec9.html (198 words)

	d03edf (Site not responding. Last check: 2007-10-25)
		A zero guess may be supplied if no better approximation is available.
		A 'smoother' based on incomplete Crout decomposition is used to eliminate the high frequency components of the error.
		A restriction operator is then used to map the system on to a sequence of coarser grids.
	www.nag.com /nagware/mt/doc/d03edf.html (380 words)

	Choleski (Site not responding. Last check: 2007-10-25)
		Symmetric matrices, positive definite matrices, SPD matrices, Cholesky decomposition, LDL
		LU factorization for SPD matrices and its relation to Cholesky decomposition, LDL
		Due to symmetry, Cholesky decomposition requires only half the amount of work as LU Cholesky decomposition breaks down if the matrix has a negative pivot
	www.math.byu.edu /~schow/work/choleski.htm (47 words)

	Department of Mathematics (Site not responding. Last check: 2007-10-25)
		The graph of the number of correct decimal places against the number of iterations results in a parabola (Newton's method) and in a piecewise linear function which can be approximated roughly by a straight line (bisection) in accordance with the convergence rate of the methods.
		Discussion: Different methods of LU decomposition are compared.
		The exercise illustrates what happens in each iteration and how a given matrix becomes a product of lower and upper triangular matrices.
	www3.it.deakin.edu.au /~gleb/pnatext.htm (1381 words)

	Newmat10 documentation
		The matrix LU decomposition is from Golub, G.H. and Van Loan, C.F. Matrix Computations, published by Johns Hopkins University Press.
		For an example of the use of this decomposition see the file example.cpp.
		Remember that an eigenvalue decomposition is not completely unique - see the comments about the SVD decomposition.
	www.ccp14.ac.uk /ccp/web-mirrors/objcryst/ObjCryst/newmat.htm (13411 words)

	How to Solve System of Simultaneous Equations, with computer programs
		It uses "Lower and Upper Triangular Decomposition of a matrix", and is also called "Crout Reduction Method"
		Exercise : Given a 4 by 4 matrix, and suppose it can be decomposed into Lower and Upper Triangular form (i.e.
		All the methods described in this webpage, "Gauss Elimination", "Crout LU Decomposition", may be used for matrix of complex numbers too, or even matrix whose elements are from a field, because what we need are properties of addition, multiplication, and the existence of inverse of non-zero element.
	balder.prohosting.com /sywu/Lequation_pg.htm (2186 words)

	General matrix (Site not responding. Last check: 2007-10-25)
		Given this decomposition, lubksb solves the system Ax=b.
		Note that if you need to solve several systems of the form Ax=b with different b's, you need call the decomposition only once, and then make repeated calls to the back substitution routine.
		A quick estimate shows the decomposition takes about
	www.math.buffalo.edu /~pitman/courses/mth437/na2/node5.html (226 words)

	Command Summary
		CHOL Computes Cholesky decomposition, X = Y'Y. CHOLDN Performs Cholesky downdate on an upper triangular matrix.
		QQR QR decomposition: returns Q1 and R. QQRE QR decomp: returns Q1, R and a permutation vector E. QQREP QR decomp.
		INV uses Crout decomposition and INVPD uses Cholesky decomposition.
	faculty.washington.edu /ezivot/cmdsum.htm (3269 words)

Try your search on: Qwika (all wikis)