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Topic: Condition number

Related Topics

Inverse problem

Propagation of errors resulting from algebraic manipulations

Numerical stability

Tikhonov regularization

Numerical analysis

Singular value decomposition

Computational physics

Eigenvalue algorithm

Scientific computing

List of numerical analysis topics

Companion matrix

Elementary matrix transformations

A priori

	Condition number - Wikipedia, the free encyclopedia
		In numerical analysis, the condition number associated with a numerical problem is a measure of that quantity's amenability to digital computation, that is, how well-posed the problem is. A problem with a low condition number is said to be well-conditioned, while a problem with a high condition number is said to be ill-conditioned.
		Condition numbers for singular-value decompositions, polynomial root finding, eigenvalue and many other problems may be defined.
		Its condition number is then defined to be the maximum value of the ratio of the relative errors in the solution to the relative error in the data, over the problem domain:
	en.wikipedia.org /wiki/Condition_number (349 words)

	PlanetMath: matrix condition number
		The condition number is a measure of stability or sensitivity of a matrix (or the linear system it represents) to numerical operations.
		Matrices with condition numbers near 1 are said to be well-conditioned.
		This is version 5 of matrix condition number, born on 2002-09-28, modified 2005-08-29.
	planetmath.org /encyclopedia/MatrixConditionNumber.html (160 words)

	PlanetMath: matrix condition number is greater or equal to $1$
		PlanetMath: matrix condition number is greater or equal to $1$
		Theorem 1 The matrix condition number is greater or equal
		This is version 5 of matrix condition number is greater or equal to
	planetmath.org /encyclopedia/PropertyOfMatrixConditionNumber.html (120 words)

	Talk:Condition number - Wikipedia, the free encyclopedia
		Can someone help me with an estimate of how big a condition number actually has to be before a matrix is considered "ill conditioned?" I'm sure it's dependent on many things but I'd like to get a grasp on it.
		I'm trying to show that in a bunch of cases (200 or so) two 2D vectors are "approximately" multiples of one another.
		On average the condition number is around 2e6, and the minimum is 9e4.
	en.wikipedia.org /wiki/Talk:Condition_number (155 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		This inequality prompts the following definition of condition number of a matrix, as well as the formal statement this inequality as a condition number theorem.
		The condition number of the matrix A with respect to the max norm is
		Note the condition number theorem implies the relative error should be small provided the condition number and the r are small.
	www4.ncsu.edu /eos/users/w/white/www/white/dir1.7/sec1.7.6.html (365 words)

	CGNS Mid-Level Library - Boundary Conditions
		the boundary condition type is being specified for the family to which the boundary belongs.
		The extent of the boundary condition may be defined using a range of points or elements, or using a discrete list of all points or elements at which the boundary condition is applied.
		to define the boundary condition region (e.g., when the region is being defined by specification of vertices, but the boundary conditions are to be applied at face centers).
	www.grc.nasa.gov /WWW/cgns/midlevel/bc.html (824 words)

	SIMAX Volume 25 Issue 1
		In this paper we study the condition number of linear systems, the condition number of matrix inversion, and the distance to the nearest singular matrix, all problems with respect to normwise structured perturbations.
		We show that for a given matrix the worst case structured condition number for all right-hand sides is equal to the unstructured condition number.
		Moreover, the condition number of matrix inversion is shown to be the same for structured and unstructured perturbations, and the same is proved for the distance to the nearest singular matrix.
	epubs.siam.org /sam-bin/dbq/article/40573 (274 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		Condition: Students will be given examples in class using number lines, two color counters, paper, and pencil.
		Condition: The student will be provided examples and use their definition of opposite.
		Condition: The student will use the addition rules and be given 30 minutes of class time.
	filebox.vt.edu /users/sgreenwa/instrdes/objectives.doc (5060 words)

	Condition Variables
		Thus, a condition variable has a queue for those threads that are waiting the corresponding event to occur to wait on, and, as a result, the original monitor is extended to the following.
		Thus, this thread is suspended and is waiting for the event that is represented by the condition variable to occur.
		Therefore, wait and signal for a condition variable is very similar to the notification technique of a semaphore: One thread waits on an event and resumes its execution when another thread causes the event to occur.
	www.cs.mtu.edu /~shene/NSF-3/e-Book/MONITOR/CV.html (800 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		For instance, the condition number bounds the change of the feasible region under perturbations of the data and bounds the number of iterations an IPM takes to solve the problem.
		The computational burden of computing these condition numbers, although polynomial, is significant and limits the testing of the condition number theory to medium sized problems, by today's standards.
		Because the characterization of the condition number is ameanable to parallelization the possibility of an efficient methodology is deemed possible.
	acts.nersc.gov /events/Workshop2002/applications/ordonez.html (402 words)

	R: Estimate the Condition Number of a Matrix, QR Decomposition or Fit (Site not responding. Last check: 2007-10-13)
		An estimate of the condition number of a matrix or of the R matrix of a QR decomposition, perhaps of a linear fit.
		The condition number is defined as the ratio of the largest to the smallest non-zero singular value of the matrix.
		(the default) the condition number is estimated by a cheap approximation.
	www.nku.edu /~longa/Rweb/library/base/html/kappa.html (178 words)

	Condition Number (Site not responding. Last check: 2007-10-13)
		The condition number of a nonsingular matrix A with respect to a matrix norm is A
		If the condition number of A is `large', A is said to be ill-conditioned.
		If the condition number is near one, A is said to be well-conditioned If the condition number is one, A is said to be perfectly conditioned.
	w3.pppl.gov /~jchen/doc/condnumber.html (74 words)

	SIMP1 Data Structure (Site not responding. Last check: 2007-10-13)
		This file contains the information that is in a ‘free form’ style where the user may specify a certain ‘error’ condition and corresponding actions to perform if the condition is met.
		The field will be blank if there is no condition to be met prior to attempting this specific test.
		Condition that must be satisfied in order for the simple imputation to be attempted.
	www.census.gov /esmpd/www/steps/datastructure/simp1.htm (901 words)

	MATH2071: LAB #5: Norms, Errors and Condition Numbers (Site not responding. Last check: 2007-10-13)
		From the definitions of norms and errors, we can define the condition number of a matrix, which will give us an objective way of measuring how "bad" a matrix is, and how many digits of accuracy we can expect when solving a particular linear system.
		Condition numbers of the Frank matrix of various sizes using different norms 2 x 2 4 x 4 8 x 8 16 x 16 1-norm __________ __________ __________ __________ 2-norm __________ __________ __________ __________ inf-norm __________ __________ __________ __________
		It is positive definite and symmetric, and is fairly well-behaved in the condition number sense.
	www.math.pitt.edu /~sussmanm/2071Spring04/lab05 (2831 words)

	Operation and Use, Volume 2 (Site not responding. Last check: 2007-10-13)
		The condition subcommand displays the current state of all known conditions in the process.
		Condition variables to be listed can be specified through the parameters, or all condition variables will be listed.
		Indicates the number of threads waiting on the condition variable.
	www.pdc.kth.se:81 /doc/SP/manuals/ppe.html-3.1/d3d31mst44.html (114 words)

	LU (JMSL)
		method estimates the condition number of the matrix.
		Return an estimate of the reciprocal of the L1 condition number of a matrix.
		- This exception is thrown when (1) the lengths of the rows of the input matrix are not uniform, and (2) the number of rows in the input matrix is not equal to the number of elements in x.
	www.vni.com /products/imsl/jmsl/v20/api/com/imsl/math/LU.html (526 words)

	MATH2071: LAB #9: Norms, Errors and Condition Numbers
		From the definitions of norms and errors, we can now define the condition number of a matrix, which will give us an objective way of measuring how "bad" the Hilbert matrix is, and how many digits of accuracy we can expect when solving a particular linear system.
		We won't worry about the fact that the condition number is somewhat expensive to compute, since it requires evaluating the inverse matrix.
		Let's simply use MATLAB's estimate rcond(A) for (the inverse of) the L1 condition number, and assume that the relative error in b is eps, the machine precision.
	www.csit.fsu.edu /~burkardt/math2071/lab_09.html (1806 words)

	Approximate Matrix Inverses and the Condition Number
		All vectors are the same size and all matrices are square real matrices with the same number of rows as the vectors.
		The condition number of a nonsingular matrix A with respect to a matrix norm is
		A matrix with a high condition number is said to be ill-conditioned.
	efgh.com /math/invcond.htm (486 words)

	CLHS: Function ERROR (Site not responding. Last check: 2007-10-13)
		(define-condition not-a-number (error) ((argument :reader not-a-number-argument :initarg :argument)) (:report (lambda (condition stream) (format stream "~S is not a number." (not-a-number-argument condition))))) => NOT-A-NUMBER (if (numberp a) (1+ a) (error 'not-a-number :argument a)) >> Error: FRED is not a number.
		Handlers for the specified condition, if any, are invoked and might have side effects.
		Those kinds of errors, while beyond the scope of the condition system to formally model, are not beyond the scope of things that should seriously be considered when writing code that could have the kinds of sweeping effects hinted at by this example.
	www.lisp.org /HyperSpec/Body/fun_error.html (439 words)

	SPIE Bookstore
		A common method used to limit the condition number of this matrix is to reject all higher order modes when the condition number reaches the maximum desired value.
		Unfortunately, computing the condition number of the gradient matrix for all possible combinations of modes is prohibitive.
		A bound on the condition number of the gradient matrix is imposed.
	bookstore.spie.org /index.cfm?fuseaction=DetailPaper&ProductId=550080&coden= (270 words)

	Condition number at opensource encyclopedia (Site not responding. Last check: 2007-10-13)
		For example, the condition number associated with the linear equation $Ax = b$ gives a bound on how inaccurate the solution $x$ will be after numerical solution.
		The condition number also amplifies the error present in $b$ .
		The extent of this amplification can render a low condition number system (normally a good thing) inaccurate and a high condition number system (normally a bad thing) accurate, depending on how well the data in $b$ are known.
	www.wiki.tatet.com /Condition_number.html (307 words)

	[No title] (Site not responding. Last check: 2007-10-13)
		CTBCON - estimate the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm
		CTBCON estimates the reciprocal of the condition number of a triangular band matrix A, in either the 1-norm or the infinity-norm.
		NORM (input) CHARACTER1 Specifies whether the 1-norm condition* number or the infinity-norm condition number is required: = '1' or 'O': 1-norm; = 'I': Infinity-norm.
	www.ibiblio.org /gferg/ldp/man/manl/ctbcon.l.html (311 words)

	Conditioning (Site not responding. Last check: 2007-10-13)
		The relationship between forward and backward error for a problem is governed by the conditioning of the problem, that is, the sensitivity of the solution to the perturbations in the data.
		If x or f is a vector then the condition number is defined in a similar way using norms (we will cover them later in the course) and it measures the maximum relative change.
		The condition number of a problem is always greater than or equal to one.
	www.cs.unc.edu /~dm/UNC/COMP205/LECTURES/ERROR/lec23/node6.html (169 words)

	Complexity & Condition Numbers in Convex Optimization (Site not responding. Last check: 2007-10-13)
		Renegar's condition number, which measures how well conditioned the data is for a convex program in conic form, is a relevant measure of the efficiency of solving a convex program via the ellipsoid algorithm.
		This presentation explores upper and lower bounds on certain geometric properties of feasible regions of convex programs and the relationship between these bounds and the condition number for convex programs developed by Renegar (which measures how well conditioned the data is for a convex program in conic form).
		This complexity is understood in terms of iterations and in terms of numerical precision requirements, and we show that it increases linearly with the logarithm of the 'condition number' of the problem instance.
	www.informs.org /Conf/Atlanta96/TALKS/TD03.html (270 words)

	Citebase - Condition number bounds for problems with integer coefficients (Site not responding. Last check: 2007-10-13)
		Condition number bounds for problems with integer coefficients
		An apriori bound for the condition number associated to each of the following problems is given: general linear equation solving, minimum squares, non-symmetric eigenvalue problems, solving univariate polynomials, solving systems of multivariate polynomials.
		Then condition numbers are bounded in terms of the dimension and of the bit-size of the input.
	citebase.eprints.org /cgi-bin/citations?id=oai:arXiv.org:math/9904128 (328 words)

	PistolsCartridge (Site not responding. Last check: 2007-10-13)
		Matching serial numbers (the numbers are stamped on the frame, barrel and cylinder only, which is correct for this type of revolver).
		All matching serial numbers (the numbers are stamped on the frame, on the barrel housing and on the cylinder).
		The serial number is within the range of numbers of the revolvers imported to the USA during the Civil War (25,000-37,000).
	www.collectiblefirearms.com /PistolsCartridge.html (7092 words)

	Norms and Condition Numbers of a Matrix
		Verify that the Frobenius norm satisfies the conditions of the matrix norm.
		The condition number corresponding to the Frobenius norm will be denoted k
		Let us see how the almost singularity (the value of the determinant is close to zero) and ill condition of the matrix are related.
	www.cs.ut.ee /~toomas_l/linalg/lin1/node18.html (377 words)

	Information Bridge: DOE Scientific and Technical Information (Site not responding. Last check: 2007-10-13)
		This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume.
		We use this shape measure to formulate two optimization objective functions that are differentiated by their goal: the first seeks to improve the average quality of the tetrahedral mesh; the second aims to improve the worst-quality element in the mesh.
		Because the element condition number is not defined for tetrahedral with negative volume, these objective functions can be used only when the initial mesh is valid.
	www.osti.gov /bridge/product.biblio.jsp?osti_id=11915 (284 words)

	Optimization Online - On an Extension of Condition Number Theory to Non-Conic Convex Optimization
		Although any convex problem can be transformed to conic form, such transformations are neither unique nor natural given the natural description of many problems, thereby diminishing the relevance of data-based condition number theory.
		Herein we extend the modern theory of condition numbers to the problem format (GP_d).
		As a byproduct, we are able to state and prove natural extensions of many theorems from the conic-based theory of condition numbers to this broader problem format.
	www.optimization-online.org /DB_HTML/2003/02/608.html (199 words)

	Rare Succulent Plants & Books: May 2004
		Set is in good+ condition with shelf wear on bottom covers, some corners are worn through, age toning to the pages, musty smell, staining to covers and in one volume 3 of the color prints were attached to opposite page in small ¾" areas which when removed detached a small amount of the 3 prints.
		The 4-volume set is in very good condition with slight damp stains and wrinkling to the first third of volume one, on the outer inch of the pages and affecting the first color plate.
		Volume one is good condition with fraying to bottom of spine and corners and has two (cacti pictures) of the three missing pictures.
	www.cactus-cacti.com /cactus-patch (13627 words)

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