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Topic: Orders of approximation

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	NationMaster - Encyclopedia: Orders of approximation
		A zeroth order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be constant, or a flat line with no slope.
		A second order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be a parabola.
		Approximation theory is a branch of mathematics, a quantitative part of functional analysis.
	www.nationmaster.com /encyclopedia/Orders-of-approximation (491 words)

	Approximation Summary
		Approximations may be used because incomplete information prevents use of exact representations.
		The type of approximation used depends on the available information, the degree of accuracy required, the sensitivity of the problem to this data, and the savings (usually in time and effort) that can be achieved by approximation.
		Approximation theory is a branch of mathematics, a quantitative part of functional analysis.
	www.bookrags.com /Approximation (1314 words)

	Worst-Case Analysis
		Increasing dash length corresponds to increasing order of approximation.
		At all orders 0-2 the worst-case distribution is shifted toward higher values relative to the corresponding average-case distribution.
		For both 0th- and 1st-order approximation, as the sub-sample size is increased, the indicated worst-case performance worsens.
	www.santafe.edu /~hag/class/node31.html (927 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal
		Orders of approximation have been used not only in science, engineering, and other quantitative disciplines to make approximations with various degrees of precision but also more generally, and more loosely, to indicate relative precision outside these disciplines in the form of "first level", "second level" and so on, "approximations".
		A zeroth-order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be constant, or a flat line with no slope.
		A second-order approximation of a function (that is, mathematically determining a formula to fit multiple data points) will be a parabola.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Orders_of_approximation (368 words)

	LongLocks HairSticks: Hair Sticks, Hair Accessories, and Jewelry Ordering Information
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	Order of magnitude Summary
		Thus, an order of magnitude is an approximate position on a logarithmic scale.
		For example, an order of magnitude estimate for a variable between about 3 billion and 30 billion (such as the human population of the Earth) is 10 billion.
		An order of magnitude estimate is sometimes also called a zeroth order approximation.
	www.bookrags.com /Order_of_magnitude (731 words)

	Approximation - Wikipedia, the free encyclopedia
		Approximations may be used because incomplete information prevents use of exact representations.
		The type of approximation used depends on the available information, the degree of accuracy required, the sensitivity of the problem to this data, and the savings (usually in time and effort) that can be achieved by approximation.
		Approximation theory is a branch of mathematics, a quantitative part of functional analysis.
	en.wikipedia.org /wiki/Approximation (500 words)

	Order of magnitude information information - Search.com (Site not responding. Last check: )
		Thus, an order of magnitude is an approximate position on a logarithmic scale.
		For example, an order of magnitude estimate for a variable between about 3 billion and 30 billion (such as the human population of the Earth) is 10 billion.
		An order of magnitude estimate is sometimes also called a zeroth order approximation.
	c10-ss-1-lb.cnet.com /reference/Order_of_magnitude (528 words)

	retromodern.com \| store policies
		Orders needing express shipping quotes must be placed by 2PM ET to be processed the same day.
		Lead times for special orders vary by manufacturer and are meant as an approximation not a guarantee.
		Orders for in stock merchandise may be cancelled within 1 business day for full refund (please allow 10 business days for processing).
	www.retromodern.com /customer_service.asp (917 words)

	Statistical Properties of Markov Classes of r=2 Rules
		It is demonstrated below that both the accuracy with which the Markov approximation predicts the properties of rules in a class, and the homogeneity of classes increases with order of approximation.
		Consider an ideal case in which all classes at a given order are sampled, all rules in each class have exactly the same properties (perfect homogeneity), and these properties are exactly those predicted by that order of approximation (perfect accuracy).
		In this case, the distribution of some property over all rules could be found by determining that property using the approximation for each class, and weighing the result by the number of rules in the class.
	www.santafe.edu /~hag/class/node18.html (681 words)

	Shopping Cart - Jan's Jewelry Supplies
		Orders paid for with US money orders will be placed with the other orders in the order they were paid, not ordered.
		After the two weeks the orders will be placed with the other orders in the order they were paid (cleared), not ordered.
		Unpaid orders, will be placed back into inventory after two week have passed.
	www.jansjewels.com /orders.html (1823 words)

	[Prosig.com] FREQUENCY, HERTZ & ORDERS
		First order is a frequency which is the same as the shaft rotational speed.
		The reason is of course that the order remains constant with shaft speed; first order is always at the shaft speed; second order is always twice shaft speed and so on.
		We do not have to sample synchronously to get orders because we can use the relationship between frequency in Hz, f, order number, OR, and rotational speed, R. The procedure is then to FFT the time history, and by using the rotational speed to convert the frequency in Hz to a 'frequency' in Orders.
	www.prosig.com /signal-processing/FrequencyHertzOrders.html (1765 words)

	Orders of magnitude
		An order of magnitude is a factor of ten.
		Orders of magnitude are quite easily and commonly described through the use of scientific notation and powers of ten.
		An order of magnitude estimate is not concerned with the precise value, but instead with the number of decimal digits after the first.
	www.fact-index.com /o/or/orders_of_magnitude.html (318 words)

	Order of magnitude - Wikipedia, the free encyclopedia
		Colloquially, the phrase orders of magnitude is usually used to describe a value that is many times larger than the value to which it is being compared.
		More precisely, the order of magnitude of a number can be defined in terms of the common logarithm, usually as the integer part of the logarithm, obtained by truncation.
		An order of magnitude estimate of a variable whose precise value is unknown is an estimate rounded to the nearest power of ten.
	en.wikipedia.org /wiki/Orders_of_magnitude (942 words)

	Order - Wikipedia, the free encyclopedia
		Order (biology), a rank between class and family, or a taxon at that rank
		Order theory, a branch of mathematics that studies various kinds of binary relations known as orders
		Order (organization), an organization of people united by a common fraternal bond or social aim.
	en.wikipedia.org /wiki/Order (309 words)

	9.6 Accuracy of the post-Newtonian approximation
		The latter question is pertinent because the ICO represents a point in the late stage of evolution of the binary which is very relativistic (orbital velocities of the order of 50% of the speed of light).
		Indeed the very essence of an approximation is to cope with our ignorance of the higher-order terms in some expansion, but the higher-order terms are precisely the ones which would be needed for a satisfying answer to these problems.
		For the present discussion we take the pessimistic view that the order of magnitude of an approximation represents also the order of magnitude of the higher-order terms which are neglected.
	relativity.livingreviews.org /Articles/lrr-2006-4/articlesu22.html (2092 words)

	The Born-Oppenheimer Approximation
		Of course, the problem cannot actually be solved exactly, so approximation methods are needed and it is in the development of approximation methods and an analysis of their accuracy that quantum chemistry is focused.
		We first invoke the Born-Oppenheimer approximation by recognizing that, in a dynamical sense, there is a strong separation of time scales between the electronic and nuclear motion, since the electrons are lighter than the nuclei by three orders of magnitude.
		This, of course, is an approximation, since there could be non-adiabatic effects that do not allow the electrons to follow in this ``instantaneous'' manner, however, in many systems, the adiabatic separation between electrons and nuclei is an excellent approximation.
	www.nyu.edu /classes/tuckerman/quant.mech/lectures/lecture_10/node1.html (1048 words)

	Single field form: introducing the notion of transformation to modal basis
		And, it is based on the unique selection of the weighted time fields as the solution obtained by setting the adjoint operator equal to zero of the reduced form of the semi-discretized system as the associated integration factor or the Green's function, respectively.
		The Generalized VIP representation allows the calculation of the dynamic response of damped systems, with proportional (Rayleigh) damping, according to equation (3.18), with the amplification matrix and the load vector defined by equations (3.19) and (3.20) respectively.
		The approximation yields the algorithm to be second-order accurate, as described subsequently.
	www-users.cs.umn.edu /~xiangmin/arc/node34.html (633 words)

	PlanetMath: Taylor series
		Both are useful to linearize or otherwise reduce the analytical complexity of a function.
		They are also useful for numerical approximation of functions, when the magnitude of the later terms fall off rapidly.
		- for the "Taylor's Theorem", $R_n$ refers to the rest of the approximation by a serie of n terms (thus a polynom of order n-1).
	planetmath.org /encyclopedia/TaylorSeries.html (798 words)

	Multivariate Approximation and Applications - Cambridge University Press
		Multivariate approximation theory is today an increasingly active research area.
		Approximation theory in the multivariate setting has many applications including numerical analysis, wavelet analysis, signal processing, geographic information systems, computer aided geometric design and computer graphics.
		This advanced introduction to multivariate approximation and related topics consists of nine articles written by leading experts surveying many of the new ideas and their applications.
	www.cambridge.org /catalogue/catalogue.asp?isbn=0521800234 (333 words)

	Class Average Distance
		It is clear, however, average predictions tend to improve with increase in order of approximation.
		Then it was demonstrated in subsection xxx that the nearer the invariant measure of a class is to the standard measure the better, on average, the Markov estimates of that invariant measure.
		Hence, for this sampling distribution, lower orders of theory should yield smaller values for the distribution over rules of average distance in figure 3.
	www.santafe.edu /~hag/class/node29.html (426 words)

	pade :: Functions (Control System Toolbox)
		is the vector of approximation orders for the input channel
		is the vector of approximation orders for the output channel
		Compute a third-order Padé approximation of a 0.1 second I/O delay and compare the time and frequency responses of the true delay and its approximation.
	www.mathworks.com /access/helpdesk/help/toolbox/control/ref/pade.html (251 words)

	How to order printed plastic bags printed tape bubble bags resealable plastic bags from Plus Packaging
		Your order will be confirmed with you before your credit card is charged.
		You will be advised of freight charges (or given an approximation), and billed for that exact amount when invoice is sent.
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	Research Articles
		On Lp approximation of functions whose r-th derivative is of bounded variation, Studia Scientiarum Math.
		Pointwise approximation by polynomials and splines, in "Proceedings of the Conference on Constructive Function Theory, Kaluga", Academy of Science USSR, Moscow, 1975, 132-141.
		Degree of nonlinear approximation, in "Approximation VI", eds.
	www.math.sc.edu /~devore/publications/ResearchArticles.html (2096 words)

	pade (Control System Toolbox)
		Such approximations are useful to model time delay effects such as transport and computation delays within the context of continuous-time systems.
		This exponential transfer function is approximated by a rational transfer function using the Padé approximation formulas [1].
		These approximation orders are given by the arrays of integers
	www.tau.ac.il /cc/pages/docs/matlab/help/toolbox/control/pade.html (248 words)

	EPDA - Dissertationen: Maurer, Markus
		In this thesis we study computational problems in a real quadratic order O. In particular, we study algorithms for computing the regulator and the fundamental unit of O, for deciding equivalence of O-ideals, and for determining generators of principal O-ideals.
		However, the analysis of the algorithms does not determine the precision of approximation necessary for the algorithms to be correct.
		In this thesis we give complete descriptions, correctness proofs, and complexity analyses of the important algorithms for approximating regulators, computing fundamental units, deciding ideal equivalence, and computing generators of principal ideals of quadratic orders.
	elib.tu-darmstadt.de /diss/000087 (418 words)

	Journal of Approximation Theory
		Approximation properties of recursively defined Bernstein-type operators (243--269).
		On the measure of approximation for some linear means of trigonometric Fourier series (193--208).
		Asymptotics of diagonal Hermite-Pad\'e approximants to $e^z$ (283--298).
	www.numerik.uni-kiel.de /journals/approx.html (611 words)

	Collect stamps and coins - sales index
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	NEA-0896: FINELM, MultiGroup Diffusion in 3-D by Finite Elements Method
		Distinct orders of approximations may be used along each axis for rectangles.
		In addition, for internal boundary conditions, distinct albedos along each coordinate axis may be specified in order to model the total leakage more exactly and to compensate for the shape of the element.
		TYPICAL RUNNING TIME - Running time is a function of the number of nodes, the orders of approximation, the order of space, the number of energy groups, the width of the up- and down-scatter bands, the usage/non-usage of coarse-mesh rebalancing, the usage/non-usage of Lebedev acceleration, and the number and type of dissections.
	www.nea.fr /abs/html/nea-0896.html (930 words)

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