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Topic: Householder transformation

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	Householder transformation - Wikipedia, the free encyclopedia
		In mathematics, a Householder transformation in 3-dimensional space is the reflection of a vector in a plane.
		The Householder transformation was introduced in 1958 by Alston Scott Householder.
		Householder reflections can be used to calculate QR decompositions by reflecting first one column of a matrix onto a multiple of a standard basis vector, calculating the transformation matrix, multiplying it with the original matrix and then recursing down the (i, i) minors of that product.
	en.wikipedia.org /wiki/Householder_transformation (248 words)

	[No title]
		In the first challenge, the household estimates consistent with the 1990 census as enumerated included data only for the total number of U.S. households by 5-year age groups; specific details, such as type of household and marital status of householder, required to project the future household composition, were not available.
		Since householders and spouses in married-couple families are limited to the population who are ever married, projections of married-couple families require projections of the marital status (never married and ever married) of the future household population.
		The universe for female family households, male family households, and nonfamily households is the total population in households minus the population in married-couple households (husbands and wives).
	www.census.gov /population/methods/p251129.txt (2865 words)

	Reduction to lower (upper) semiseparable form
		Finally, a Householder transformation has to be performed to the left to have a complete upper triangular semiseparable structure.
		Note that the computational complexity of applying the Householder transformations is the same as of the standard procedure that reduces matrices into bidiagonal form using Householder transformations.
		The purpose of these Givens transformations is to chase the bulge on the subdiagonal upwards while maintaining the upper triangular semiseparable structure in the upper part of the matrix.
	www.cs.kuleuven.ac.be /~raf/homepage/publications/phd/node48.html (700 words)

	QR decomposition - Wikipedia, the free encyclopedia
		There are several methods for actually computing the QR decomposition, such as by means of Givens rotations, Householder transformations, or the Gram-Schmidt decomposition.
		A Householder reflection (or Householder transformation) is a transformation that takes a vector and reflects it about some plane.
		This can be used to gradually transform an m-by-n matrix A to upper triangular form.
	en.wikipedia.org /wiki/QR_decomposition (1058 words)

	Householder (Site not responding. Last check: 2007-10-31)
		Prem is told by a swami (Pahari Sanyal, far right) that, as a householder with much work to do in the world, he must not...
		A Householder transformation is a rank-1 modification of the...
		Related: householder :: householders and the use of force against intruders :: householder group :: householder transformation :: householder matrix :: householders and the use of force :: householders rights :: householder reflection :: householders :: householder method
	www.logicjungle.com /wiki/Householder (234 words)

	Householder - Wikipedia, the free encyclopedia
		A householder is a person who is the head of a household; see House.
		In mathematics, there exists a Householder transformation, named after Alston Scott Householder.
		This is a disambiguation page: a list of articles associated with the same title.
	en.wikipedia.org /wiki/Householder (95 words)

	Fourth Homework (Site not responding. Last check: 2007-10-31)
		In part b you were asked to find a Householder transformation that annihilates the third component of the vector a.
		In parts d and e you were asked whether or not a Householder transformation could ever be the same as an elementary elimination matrix or a Givens rotation when annihilating a given nonzero component of a vector.
		In both cases the answer is no because a Householder transformation is represented by a symmetric matrix while the other 2 are represented by nonsymmtric matrices.
	www.rpi.edu /~lvovy/Fall2005/node56.html (246 words)

	Householder method
		Householder method is method used for reducing the n-dimensional square matrix to an upper Hessenberg matrix, or into tridiagonal form, if input matrix is Hermitean.
		Class implements two types of algorithms, depending of user input, one does the transformation considering column by column of input matrix, and the other one takes row by row.
		Each transformation in algorithm annihilates the required part of a matrix column/row, so procedure is carried out by the n-2 orthogonal transformations.
	www.matf.bg.ac.yu /r3nm/NumericalMethods/EigenValues/Householder.html (103 words)

	Householder (Site not responding. Last check: 2007-10-31)
		Alston Householder spent his childhood in Alabama where his family had moved shortly after he was born.
		To present a basic algorithm for the QR factorization, we must start by introducing Householder transforms (reflections).
		Householder transformations zero the elements of a column vector below the first element: with.
	www.bigletterlist.net /w/h/Householder.htm (327 words)

	Householder - Householder transformation: Information From Answers.com
		HOUSEHOLDER AWARD XI Nominations are solicited for the Alston S. Householder Award XII.
		Jake Householder - Acoustic Emo with a Purpose
		Householder transformation In mathematics, a Householder transformation in 3-dimensional space is the reflection of a vector in a plane.
	scoutwide.com /?q=householder (193 words)

	Householder Transformation Method
		Householder's method is used to construct a similar symmetric tridiagonal matrix.
		The second Householder transformation is applied to the matrix
		We now present a version of the Householder program that uses traditional more traditional loops to perform the computations.
	math.fullerton.edu /mathews/n2003/HouseholderMod.html (358 words)

	JSpline+ API Specification: Class Reflection
		Constructs the Householder bearing vector inplace of the vector to be transformed, prepares the instance for the transformation with the constructed vector, and returns the value c of the first vector's entry after the transformation.
		Constructs the Householder transform on the first column of the dense matrix, writes the bearing vector inplace of the first column, applies the transform to other columns of the matrix, and returns the value c of the first matrix entry after the transformation.
		- the pointer to the vector to be transformed
	www.excelsior-usa.com /doc/jspline/api/ru/sscc/util/Reflection.html (548 words)

	Householder Transformations - GNU Scientific Library -- Reference Manual
		A Householder transformation is a rank-1 modification of the identity matrix which can be used to zero out selected elements of a vector.
		The functions described in this section use the rank-1 structure of the Householder matrix to create and apply Householder transformations efficiently.
		This function prepares a Householder transformation P = I - \tau v v^T which can be used to zero all the elements of the input vector except the first.
	gnu.org /software/gsl/manual/html_node/Householder-Transformations.html (189 words)

	3
		Thus, in a sense it is not a perturbation method, but a transformation method, which may be viewed as a new type of matrix - a
		Superficially, the method resembles a Galerkin formulation which has its origin in a completely different philosophy, namely in demanding that any subset of a complete set used to expand an exact solution must be orthogonal to those states not included in the expansion - the residuals.
		The product of Householder transformations that leads to a tridiagonal form is a similarity transformation, and thus eigenvalues of the tridiagonal matrix are the same as the original matrix.
	www.ucs.louisiana.edu /~nxs7560/varsp.html (2643 words)

	Householder - Find The Best Householder Resources Online (Site not responding. Last check: 2007-10-31)
		Householder method is method used for reducing the n-dimensional square matrix to
		Householder and Cannon both said they were misrepresented in the article.
		Householder is a resident of Park Ridge, Illinois and a certified public accountant in Between 1976 and 1999, Householder was associated with several
	argon.infoseekengine.com /pise/argon-householder.html (698 words)

	Constrained and Unconstrained Linear Least Squares Fitting
		The solution is found by Householder triangularisation (see Ref. 1 for details) with parameter elimination if constraints are present.
		it is found by applying successive Householder transformations (Q) which reduce A to upper triangular form without changing the norm of the columns of A or the vector b.
		An attractive feature of the unitary Householder transformations is that when each parameter is eliminated ("solved for") column pivoting allows the selection of that parameter which gives the maximum reduction in the current value of
	wwwasdoc.web.cern.ch /wwwasdoc/shortwrupsdir/e230/top.html (673 words)

	GAMS : Problem Taxonomy
		Transform (search also classes L10a1, N6, and N8) L2b.
		Spectrum estimation using the Fourier transform of the autocorrelation function L10a3a5.
		Cross-spectrum estimation using the Fourier transform of the cross-correlation or cross-covariance function L10b3a6.
	gams.nist.gov /Classes.html (718 words)

	Evolutionary profiles from the QR factorization of multiple sequence alignments -- Sethi et al. 102 (11): 4045 Data ...
		The effect of the Househoulder transformation is to reflect the vectors about the dotted line.
		The dotted line is the bisector of the angle between the vector a and the —x-axis, i.e., the axis of the first unit vector.
		The Householder transformation is also applied to the two vectors b and c.
	www.pnas.org /cgi/content/full/0409715102/DC1 (439 words)

	The reduction to upper triangular semiseparable form
		The first step consists of applying a Householder transformation or a sequence of Givens transformations to annihilate all the elements of the vector
		We choose to annihilate the elements with a Householder transformation
		The next step consists of applying another Householder transformation on the left of the matrix (6.6) such that:
	www.cs.kuleuven.ac.be /~raf/homepage/publications/phd/node68.html (377 words)

	[No title] (Site not responding. Last check: 2007-10-31)
		M the transformation will be constructed to C zero elements indexed from L1 through M. If L1 GT.
		C C() On entry to H1 or H2 C() contains a matrix which will be C regarded as a set of vectors to which the Householder C transformation is to be applied.
		C NCV Number of vectors in C() to be transformed.
	www.netlib.org /slatec/src/h12.f (286 words)

	Matlab File: QR factorization with Householder (Site not responding. Last check: 2007-10-31)
		To compute the QR factorization of an arbitrary (n x m)-matrix A with R=QA, where Q is a orthogonal matrix and R an upper triangle matrix, use the command
		The resulting matrix B contains in the upper triangle the matrix R and in each column the necessary information for the Householder vector v of the corresponding Householder transformation.
		We remark, that the Householder vector is scalled in such a way, that the first component is equal to 1.
	matlabdb.mathematik.uni-stuttgart.de /download.jsp?MC_ID=3&MP_ID=164 (98 words)

	[No title]
		SUBROUTINE TR2(A, LDA, U, S, I1, I2, J1, J2) C C PURPOSE: C The subroutine TR2 performs the Householder transformation C H = I - S x UU' on the columns J1+1 to J1+J2 of matrix A, this C from rows I1 to I2.
		C Contains the submatrix of A onto which the Householder C transformation H is applied.
		C Contains the transformation vector of the transformation C matrix H. C Contains the scalar S of the transformation matrix H. C Contains the first row index of A (see purpose).
	www.netlib.org /vanhuffel/tr2.f (237 words)

	Householder Reflection
		The Householder matrix H is symmetric and orthogonal.
		It is significant to note that the Householder matrix H depends only on the direction of Householder vektor
		and according to it the Householder transformation that annihilates the two last coordinates of the vector
	www.cs.ut.ee /~toomas_l/linalg/lin2/node6.html (175 words)

	Householder - Socialism, Inflation, and the Thrifty Householder (Site not responding. Last check: 2007-10-31)
		This is the text of the Criminal Law (Amendment) (Householder Protection) Bill, as ordered by the House of Commons to be printed on 12th January 2005.
		QR factorization with Householder Q = Q_HOUSE(B) from the matrix B. Keywords:, QR factorization, Householder transformation.
		The Ludwig von Mises Institute is the research and educational center of classical liberalism and the Austrian School of economics.
	webinfofeed.com /wifd/householder.htm (440 words)

	Nonlinear Solver Project: LOCA::Continuation::HouseholderGroup Class Reference
		Computes the Householder vector from the predictor vector.
		Since the Householder projection method does not use the arc-length equation in the Newton solve, we set the residual for the arc-length equation to zero.
		The algorithm employed here is taken from Algorithm 5.1.1 from Gene Golub and Charles Van Loan, "Matrix Computations", 3rd Edition, 1996, John Hopkins University Press, Baltimore.
	software.sandia.gov /nox/classLOCA_1_1Continuation_1_1HouseholderGroup.html (196 words)

	GNU Scientific Library -- Reference Manual - Linear Algebra (Site not responding. Last check: 2007-10-31)
		The algorithm used to perform the decomposition is Householder QR with column pivoting (Golub & Van Loan,
		This function solves the system A x = b directly using Householder transformations.
		This function solves the system A x = b in-place using Householder transformations.
	www.jamesthornton.com /gnu/gsl/gsl-ref_13.html (2897 words)

	Grabbing the nearest book by Books Blog
		“Each Householder transformation must be applied to the remaining unreduced portion of the matrix, but it will not affect the prior columns already reduced, and hence the zeros are preserved through successive transformations.”
		This entry was posted on Friday, December 17th, 2004 at 12:23 pm and is tagged with householder transformation, book lovers, numerical analysis, zeros, transformations, grabbing, grab, columns, and journal.
		You can follow any responses to this entry through the RSS 2.0 feed.
	books.elliottback.com /archives/2004/12/17/grabbing-the-nearest-book (521 words)

	Mailgate: sci.math.num-analysis: shortcut to tridiagonal? (Site not responding. Last check: 2007-10-31)
		The square matrix A = S' S (prime denotes transpose) can be reduced to tridiagonal form by Householder transformations, from which one can proceed to get eigenvalues in conventional fashion.
		But for large S (many rows and columns, that is), the multiply to get A is killing me computationally.
		Is there a name for the technique, if any, that one can use to find the tridiagonal form of A, given just S? Some kind of modified Householder transformation?
	mailgate.supereva.it /sci/sci.math.num-analysis/msg13759.html (116 words)

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