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Topic: Householder reflection

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Orthogonal matrix

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	Changes In Median Household Income: 1969 to 1996
		Households with a householder between 40 and 64 years old had an increase of 34 percent when the earnings of wives were counted, but an increase of 16 percent when the earnings were excluded.
		The income of these households rose 28 percent from 1969 to 1979, a period when there was a gain in the median income of all households, and rose 17 percent from 1979 to 1983, a period when there was a decline in the median income of all households.
		Among married-couple households with no children and with a householder 65 years or over, the proportion with low relative incomes was 34 percent in 1969, 19 percent in 1983, and 18 percent in 1996 (the 1983 and 1996 figures are not statistically different).
	www.census.gov /hhes/www/p23text.html (3046 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.
		Q can be used to reflect a vector in such a way that all coordinates but one disappear.
	en.wikipedia.org /wiki/QR_decomposition (846 words)

	REFLECTIONS ON VIOLENCE, GUNS, AND THE DEFENSIVE USE OF LETHAL FORCE
		Suppose the householder, hearing the intruder, retrieves his deer rifle from under the bed, creeps silently down the stairs, and draws a bead on the back of the intruder's head from a range of three meters.
		Truncating the householder's use of deadly force probably would, by reducing one of the occupational hazards of housebreaking, lead to more burglary, and thus reduce the caution housebreakers now take to strike only when they believe dwellings are unoccupied.[63] More housebreaking would seem unavoidably to lead to more confrontations between intruders and householders.
		Although the householder, divested of his gun and his privilege to use it, might personally pose less of a threat to the intruder than he would with both gun and privilege, the householder still represents a threat that a rational intruder would surely respect.
	www.saf.org /LawReviews/LawProbPolsby.htm (10521 words)

	[No title]
		Householder reduction algorithm, on the other hand, is provably numerically stable.
		Householder sequential reduction algorithm takes twice as many arithmetic operations comparing with Gaussian elimination.
		Based on sequential Householder reduction algorithm and corresponding reflection theory as a geometric interpretation of this algorithm, prepare parallel version of this algorithm, implement in selected parallel/distributed programming environment, and compare with Gaussian elimination algorithm in terms of parallel execution time, speedup, and efficiency.
	www.cis.umassd.edu /~bmikolajczak/CIS575/project.htm (184 words)

	Mediation in the planning system (Site not responding. Last check: 2007-10-15)
		The airing of all the issues in dispute through the means of mediation can often lead to a degree of satisfaction for both parties through the realisation that absolutely every issue in a dispute has been opened up and explored in depth, on a confidential basis.
		A 'householder' application is one which is for the extension or alteration of a single dwelling house.
		4.3.2 The dominance of 'householder' cases and the sparse distribution of the remaining cases over seven other development categories means that the results of any analysis are primarily relevant to 'householder' cases.
	www.odpm.gov.uk /stellent/groups/odpm_planning/documents/page/odpm_plan_606548-06.hcsp (2170 words)

	World Almanac for Kids
		The three original ashramas were the chaste student (brahmachari), the householder (grihastha), and the forest-dweller (vanaprastha).
		They were said to owe three debts: study of the Vedas (owed to the sages); a son (to the ancestors); and sacrifice (to the gods).
		Shiva is also the deity whose phallus (linga) is the central shrine of all Shaiva temples and the personal shrine of all Shaiva householders; his priapism is said to have resulted in his castration and the subsequent worship of his disembodied phallus.
	www.worldalmanacforkids.com /explore/religion/hinduism.html (4034 words)

	Matrix Reference Manual: Special Matrices
		Geometrically: Orthogonal matrices in 2 and 3 dimensions correspond to rotations and reflections.
		A 2#2 orthogonal matrix is either a Givens rotation or a Givens reflection according to whether it is proper or improper.
		A 3#3 orthogonal matrix is either a rotation matrix or else a rotation matrix plus a reflection in the plane of the rotation according to whether it is proper or improper.
	www.ee.ic.ac.uk /hp/staff/dmb/matrix/special.html (4190 words)

	World Religions-Jainism (Site not responding. Last check: 2007-10-15)
		A person's behavior and his actions are the reflection of his internal thoughts, day in and day out.
		They are reflections upon the fundamental facts of life, intended to develop purity of thought and sincerity in the practice of religion.
		A householder is permitted to incur violence defensively and vocationally provided he maintains complete detachment.
	www.allaboutsikhs.com /religion/jain7.htm (4061 words)

	Egwald Mathematics - Linear Algebra: Matrices and Matrix Decomposition
		Reflection matrices act as a mirror with respect to the Ø line through the origin.
		When a vector is multiplied by a reflection matrix, the vector is reflected through the Ø line an equal distant to the other side of the line.
		Householder decomposition is used on the Statistics web pages to solve least-squares (multiple regression) problems.
	www.egwald.com /linearalgebra/matrices.php (3976 words)

	Citizens for Tax Reform : repealthetax.com \| News (Site not responding. Last check: 2007-10-15)
		If this is Team Householder`s grand design for working his way to the governor`s office, it certainly is unique: Ruining one`s own reputation is not a well-established method of achieving political success.
		Householder acknowledges that the 109-page document was the work of three of his closest political advisers.
		But Householder`s enemies have no need to embarrass him as long as his friends and allies are on the job.
	www.repealthetax.com /news.aspx?ID=29 (360 words)

	[No title]
		Householder QR factorization: ----------------------------- Background Problem with basic Householder QR decomposition One drawback of the basic Householder algorithm is that it doesn't take into account the registers and cache hierarchy of modern superscalar processors.
		To improve the performance of Householder QR decomposition on modern superscalar processors, the algorithm has to consider the registers and cache hierarchy of these processors.
		Cache Householder QR decomposition The cache model for the cache Householder decomposition algorithm model is: the processor is connected to L>=2 caches; the caches are fully associative and use least-recently-used(LRU) replacement policy.
	www.cs.utexas.edu /~hmliu/project/report/progress_report.txt (1459 words)

	MATH2071: LAB #7: QR Factorizations (Site not responding. Last check: 2007-10-15)
		The other difference, which you'll have to take on faith, is that the Householder factorization is generally more accurate (smaller arithmetic errors), and easier to define compactly.
		If we have computed the Householder QR factorization of a matrix without encountering any singularities, then it is easy to solve linear systems.
		Instead of the Householder form of the factorization, we may use the Gram-Schmidt QR factorization.
	www.math.pitt.edu /~sussmanm/2071Spring04/lab07 (2414 words)

	[No title]
		A Householder reflection is a matrix of the form $$P=I-{1\over\beta}uu^\ast,\qquad \hbox{where }\beta={\u\^2\over2}.$$ $A^\ast$ denotes the conjugate transpose $(\bar A)^t$ of a complex matrix $A\in C^{m\times n}$.
		Householder reflections $P$ are Hermitian ($P^\ast=P$), unitary ($P^\ast P=I$), and self-inverse ($P^{-1}=P$).
		Then $P = I - {1\over\beta}uu^\ast$ is a Householder reflection and $Pa=-\alpha e_1$.
	ei.cs.vt.edu /~cs3414/S97/linsys.txt (754 words)

	SRIMAD BHAGAVATAM: CANTO 7 - CHAPTER 12 (Site not responding. Last check: 2007-10-15)
		He, not belonging to the householders life, must, to the as good as invincible senses that even take away the mind of a renunciate, give it up to address women with the observance of the great vow of celibacy [the yama of ashthânga-yoga].
		As long as reflection is ascertaining this positively in self-realization is there for that time freedom from illusion with the duality, but not detaching by that duality is there indeed of the person the inverse [see also
		As long as a living entity is not completely self-realized--as long as he is not independent of the misconception of identifying with his body, which is nothing but a reflection of the original body and senses--he cannot be relieved of the conception of duality, which is epitomized by the duality between man and woman.
	www.srimadbhagavatam.org /canto7/chapter12.html (3645 words)

	[No title] (Site not responding. Last check: 2007-10-15)
		Being an orthogonal transformation a Householder reflection is 2-norm preserving.
		Thus a Housholder reflection can only reflect unit vectors x "to be [the] jth column of [the] identity".
		Householder reflections are meant to apply to any nonzero vector x, not just unit vectors.
	www.octave.org /mailing-lists/bug-octave/2003/427 (139 words)

	[No title]
		Thus the householder and the ascetic are the tow wheels on which the cart of Jaina ethical discipline moves on quite smoothly.
		A little reflection will make it clear that the concept of Ahimsa belonging to the realm of ethics is a logical consequence of the ontological nature of things.
		This is manifest from the persistent emphasis laid by all the Jaina Acaryas on the veritable achievement of Samyagdarsana (spiritual conversion).
	www.jainworld.com /jainbooks/compliteethical/preface.doc (1524 words)

	Householder Transformation Method
		Householder's method is used to construct a similar symmetric tridiagonal matrix.
		We now present a version of the Householder program that uses traditional more traditional loops to perform the computations.
		This program will be harder to read, but might prove to be more efficient when the size of the matrix is larger.
	math.fullerton.edu /mathews/n2003/HouseholderMod.html (358 words)

	Matrix Manual: Special Matrices
		Multiplying a vector by a Householder transformation reflects it in the hyperplane that is orthogonal to v.
		Householder matrices are important because they can be chosen to annihilate any contiguous block of elements in any chosen vector.
		Geometrically: Orthogonal matrices correspond to rotations and reflections.
	www.psi.utoronto.ca /matrix/special.html (2192 words)

	THE HOUSEHOLDER
		In this context, this Gurbani Reflection will attempt to reflect on as to who and what the householder is, and what constitutes a "liberated" householder.
		According to the scriptures, sages, and ancient wisdom, householder or a Sansaaree is he who is wrapped up in a strong attachment to the worldliness.
		The Gurbani observes that the householder which is filled with abundance, even that household suffers anxiety.
	www.gurbani.org /webart31.htm (2886 words)

	Buddhism in Translations - § 78. The Trance of Cessation.
		Inspirations and expirations, O householder, are bodily functions, therefore inspirations and expirations constitute bodily karma; first occur reasoning and reflection and afterwards articulate utterance, therefore reasoning and reflection constitute vocal karma; perception and sensation are mental
		Therefore he must reflect on this, and so enter his trance as to rise from it of his own accord.
		He should not enter this trance without first reflecting whether his span of life is to last seven days longer or not.
	www.sacred-texts.com /bud/bits/bits078.htm (1396 words)

	[No title]
		The two optimized Householder QR algorithms proposed by Carrig and Meyer in [1] are an example.
		Cache Householder QR: Improve performance by reducing cache misses The idea In the cache Householder algorithm, instead of updating columns j+1 to n immediately after computing u(j), it performs only those updates necessary to accumulate u(j), u(j+1),..., u(j+s-1) using basic Householder algorithm.
		Like the cache Householder algorithm, it postpones the updating of the remaining columns of A. Unlike the CH algorithm, it only updates the next s columns starting from column c using the already computed c-1 columns.
	www.cs.utexas.edu /~hmliu/project/report/final_report.doc (2197 words)

	Complex Analogue of Householder Reflections: Summary (Site not responding. Last check: 2007-10-15)
		Personal reminiscences of Householder [This is a small excerpt from a wonderful letter.
		Householder always called Householder matrices > "elementary Hermitian matrices." An alternative to the Householder reflection The direct rotation introduced by Chandler Davis gives the orthogonal matrix closest to I that maps a unit vector with top entry gamma (>=0) and the rest called s into e_1.
		A S Householder: The Theory of Matrices in Numerical Analysis (Dover) 4.
	www.csc.fi /math_topics/Mail/NANET97-2/msg00158.html (485 words)

	f_orthog
		is an orthogonal matrix (because reflections are rigid).
		The matrices of reflections are also useful in numerical analysis, where they are called Householder transformations.
		Just as for rotations, it is possible to talk about reflections that do not leave the origin fixed, i.e., whose mirrors do not go through the origin.
	www.math.ucla.edu /~baker/149.1.02w/handouts/f_orthog/node5.html (189 words)

	NA01 Contributed Conference Abstracts (Site not responding. Last check: 2007-10-15)
		Householder's and Givens' transformations applied to complex vectors
		If one applies a Householder transformation H which is written for the real case to a complex vector x one might be surprised: The matrix H is still orthogonal (in the sense H H
		It turns out that the (advisable but not necessary) step one takes in the real Householder case to avoid cancellation, namely to make the calculation depend on the sign of the first component of x is a necessary step to make the computation right also in the complex case.
	www.mcs.dundee.ac.uk /~naconf/01/abstracts/SUBopfer.html (228 words)

	Matrix Manual: Special Matrices
		[22]: A 22 matrix is a Givens reflection iff it is a Householder matrix.
		[22]: A 22 matrix is Householder iff it is a Givens Reflection.
		[22]: A 22 orthogonal matrix is either a Givens rotation or a Givens reflection.
	www.ee.uwa.edu.au /~roberto/teach/matrix/special.html (2558 words)

	Artificial Reverberation (Site not responding. Last check: 2007-10-15)
		Early reflections should be calculated for a given geometry and spatialized.
		A rough guide to the average delay-line length is the ``mean free path'' of the desired reverberant environment, which is defined as the average distance a ray of sound travels before it encounters a reflecting obstacle.
		It may be useful for determining a set of early reflections in spaces with large, flat walls.
	www.music.mcgill.ca /~gary/614/week12/reverb.html (1511 words)

	June 17, 2001 (Site not responding. Last check: 2007-10-15)
		For the kingdom of heaven is like a householder who went out early in the morning to hire laborers for his vineyard.
		There are some printed materials on the back table, and I encourage you to browse through them and either introduce yourself or refresh your memory about this terrific organization.
		I was struck with a number of insightful and grace-filled observations that came up during the weekend, several of which were made by Rev. Dirk Ficca from the Council for a Parliament of the World's Religions in Chicago.
	members.aol.com /pastmessages2001/01june17.html (1998 words)

	MATH2071: LAB #10: QR Factorizations (Site not responding. Last check: 2007-10-15)
		The formulas for a Householder matrix are a little complicated, and we won't go into them here.
		A = frank (5) Q = eye (5) R = A H = householder (R, 1) Q = Q * H' R = H * R Q * R H = householder (R, 2) Q = Q * H' R = H * R Q * R...
		The other difference, which you'll have to take on faith, is that the Householder factorization is generally more accurate, and easier to define compactly.
	www.csit.fsu.edu /~burkardt/math2071/lab_10.html (3230 words)

	Jacobi-type iterative methods (Site not responding. Last check: 2007-10-15)
		This is true when a two-sided similarity transform is used but a one-sided variant is known to be more efficient in a parallel implementation.
		A one-sided tridiagonalisation, rather than the usual Householder reflection, was described by Hegland [33].
		It is also well known that Jacobi eigensolvers improve as the matrix is more diagonally dominant, quite simply there are less iterations to achieve the required accuracy.
	www.dl.ac.uk /TCSC/Subjects/Parallel_Algorithms/diagreport/node16.html (298 words)

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