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Topic: Propagation of errors resulting from algebraic manipulations

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Condition number

Numerical stability

Elementary matrix transformations

Scientific computing

Computational physics

List of numerical analysis topics

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	Publication-Abstracts by Martin Erwig
		Roughly spoken, the first level algebra defines types and operations of the query language whereas the second level algebra defines kinds (collections of types) and type constructors as functions between kinds and so provides the types that can be used at the first level.
		Multi-level algebra is capable of expressing very subtle details of type systems, such as preventing type constructors from being nested or describing operations with a variable number of arguments.
		Fortunately, the resulting specifications of algorithms, in addition to being compact and declarative, are expected to have an almost as efficient implementation as their imperative counterparts.
	web.engr.oregonstate.edu /~erwig/papers/abstracts.html (11676 words)

	Encyclopedia :: encyclopedia : Numerical analysis (Site not responding. Last check: )
		Round-off errors arise because it is impossible to represent all real numbers exactly on a finite-state machine (which is what all practical digital computers are).
		Truncation errors are committed when an iterative method is terminated and the approximate solution differs from the exact solution.
		Generally, it is important to estimate and control round-off errors arising from the use of floating point arithmetic.
	www.hallencyclopedia.com /Numerical_analysis (1599 words)

	Database manipulations using group theory - Patent 20050187905
		The result of a query is a set of zero or more pairs (g,c) where g is a group element and c is a database element, where each g(c) satisfies the property P specified by the query.
		A result construction module 220 receives the results of the one or more query executions from the query execution module 218 and converts the results from the group theory representation to the native representation of the data.
		In this case, an embodiment of the result construction module 220 analyzes the results of the low-level queries to generate an answer to the high-level query in terms familiar to the native representation of the input data.
	www.freepatentsonline.com /y2005/0187905.html (9143 words)

	Hypersystolic Reed-Solomon decoder - Patent 4958348
		Implementation of the error correction functions of syndrome generation, computation of error locator and error valuator polynomials, and application of these to the input data stream are achieved in a serialised architecture of novel structure.
		Thus state bit 40 controls multiplexer 41 in such fashion as to select for the downwardly propagating output either of the downwardly propagating input from the next higher adjacent cell or the upward propagating data of the same cell which would otherwise be directed to the upward data input of the next adjacently upward cell.
		In this manner the logical requirements for any of a class of error correcting codes of varying parameters may be accommodated in the essentially variable length hypersystolic arrays forming the component structures of the present error correcting decoder.
	www.freepatentsonline.com /4958348.html (11346 words)

	Math For Measurement
		A mix of graphical, numerical, and algebraic representations and methods are used, including examples of each approach which enable solution of problems that are more difficult with the other methods.
		The development of the course objectives, and of the tactics used to achieve them, came mainly from critical analysis (for relevance to the goals and target audience of this course) of each of several standard mathematics and science courses, as well as domain-specific vocational courses.
		While science-course demonstrations of the ability of mathematical laws to summarize and predict scientific relationships are in accord with the MFM agenda of showing the potential of mathematical thinking for practical use, the typical effect of science courses on practical-arts students is more intimidation than inspiration.
	www.schoolsupport.net /MFM/MFM_MAApaper.htm (6712 words)

	Hoax
		The velocity of propagation of a vibration in a medium is determined by the properties of the medium and is independent of the velocity of its source.
		In the proposed modification of the experiment, the independence of the results on the velocity of the laboratory through space is eliminated by moving the coincidence detector to the left side of the setup and substituting adjustable delay lines in the signal paths between the left side photon detectors and the coincidence detectors.
		For that coincidence to be observed the propagation delay of the delay lines must be adjusted to be equal to the propagation delay of the signal in the cable which couples the photon detectors at the right side to the coincidence detectors.
	users.isp.com /retic/physics/hoax.htm (19538 words)

	Class 702: DATA PROCESSING: MEASURING, CALIBRATING, OR TESTING / U.S. Patent Classification Definitions
		For the purpose of this class, data processing is defined as a systematic operation on data in accordance with a set of rules which results in a significant change in the data.
		Subject matter wherein the data processing system or calculating computer is designed for or utilized to determine the amount of a fluid mass or volume passing through a structure (e.g., conduit, pipe) per unit area or time.
		Subject matter wherein errors that arise from using different sensors or probes are corrected by using stored calibration information corresponding to respective plug-in sensors or probes.
	www.uspto.gov /web/offices/ac/ido/oeip/taf/def/702.htm (9867 words)

	Beyond separating implicit from explicit memory or learning: Toward a functional integration.
		If we transpose the results from the computational model to the level of the phenomenal consciousness of actual people, it appears that the very same process that permitted word formation during the initial stage of learning is able to generate the phenomenal experience of well-formedness for syntactically correct word sequences.
		The participants were unable to verbalize the nature of the manipulation and, in particular, they had no explicit knowledge of the subdivision into logical blocks of five trials, which was a precondition which had to be satisfied if they were to grasp the other rules.
		Reber claimed that these results testify to the fact that participants are able to abstract the "syntax" of the displayed material, independently of the "vocabulary".
	www.bbsonline.org /documents/a/00/00/22/39/bbs00002239-00/bbs.perruchet.htm (19160 words)

	Understanding Statistics: Resources and Information
		In contrast, mathematical statistics (or simply statistical theory) is the subdiscipline of applied mathematics which uses probability theory and analysis to place statistical practice on a firm theoretical basis.
		The word statistics is also the plural of statistic (singular), which refers to the result of applying a statistical algorithm to a set of data.
		Due to errors in experimental procedures, specifically the lack of a control group, the researchers while unable to do what they planned were able to provide the world with the Hawthorne effect.
	concepts.essential-facts.com /Statistics.html (2229 words)

	[No title]
		The most common approach ("wavefront propagation") partitions the traversable space into uniform-size cells, and propagates a wavefront from the starting point until it hits the goal point, a wavefront representing cells of near-equal cost from the starting point.
		The efficiency of the two approaches is not strictly comparable because their complexities are based on different units (the number of cells total for wavefront propagation, and the number of polygonal-region edges for the weighted-region approach); the algorithms of the second approach are more complicated, but they need reason about fewer entities.
		The cost error will be no greater than the cost-rate in the region times the maximum distance of the piecewise-linear approximation from the actual curve, a generally very small number.
	www.nps.navy.mil /Content/CS/ncrowe/robaut90.html (10916 words)

	[No title]
		The differences are a result of the assumptions employed and the method of computation as well as the problems involved in extrapolating data from published graphs.
		In order to obtain results that are in agreement with Schelkunoff's results and standard engineering practice it is necessary to adopt the usual circuit theory time convention of e+.
		INTRODUCTION The purpose of this section is to present numerical results for the modal and terminating admittances of a spherical dipole in an inhomogeneous, compressible plasma.
	deepblue.lib.umich.edu /bitstream/2027.42/6171/4/bac7738.0001.001.txt (13069 words)

	Interactive Statistical Calculation Pages
		The WebMath page performs a large number of numeric calculations and symbolic algebraic manipulations of the type that might arise in high school / college algebra and calculus, including some elementary statistical calculations.
		Manipulation of a correlation matrix -- you enter the N-by-N correlation matrix, the page computes all Partial Correlation Coefficients, all Standardized Partial Regression Coefficients, and the Multiple Correlation Coefficient for each variable.
		Confidence Interval Calculator to compute the margin of error and confidence interval given the population size, sample size, sample percentage, and confidence level.
	statpages.org (9718 words)

	Slinky Booklet
		It is not possible to reproduce these enormous ranges in a laboratory on Earth and study the results of controlled experiments;we must use the Universe as our laboratory in order to see how matter and energy behave in the most extreme conditions.
		Tell students that first and foremost is the fact that the velocity of the waves generated in the lab are not constant as you attempt to achieve higher and higher frequencies (i.e.,smaller and smaller wavelengths).
		When multiplied,the units for the result become ______________, which is a measure of velocity.
	swift.sonoma.edu /education/slinky_booklet (5060 words)

	Content Standards - Mathematics - FSU College of Education
		1.5.1 The mathematics teacher should represent and manipulate various types of numbers such as odd, even, perfect, square, cube, triangular, and pentagonal numbers both geometrically and algebraically using appropriate software where applicable.
		6.3.5 The mathematics teachers should pay attention to computations but put emphasis on choosing the calculation, interpreting the results, and explaining the results to others, rather than on the calculation details, which can be done rapidly by computers or calculators.
		6.3.7 The mathematics teachers should recognize the widespread application of linear algebra in other areas of mathematics such as multivariable calculus, differential equations, and probability; as well as in physics, biology, chemistry, economics, psychology, sociology, and engineering.
	saint.coe.fsu.edu /ncate/cs/csView.cfm?subject=Mathematics (5439 words)

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