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	Horner scheme - Wikipedia, the free encyclopedia
		In the mathematical subfield of numerical analysis, the Horner scheme or Horner algorithm, named after William George Horner, is an algorithm for the efficient evaluation of polynomials in monomial form.
		The Horner scheme can also be viewed as a fast algorithm for dividing a polynomial by a linear polynomial (see Ruffini's rule).
		Even though the algorithm is named after William George Horner, who described it in 1819, the method was already known to Isaac Newton in 1669, and even earlier to the Chinese mathematician Ch'in Chiu-Shao in the 13th century.
	en.wikipedia.org /wiki/Horner_scheme (516 words)

	Frederick Horner Papers (Library of Congress)
		Horner was officially listed as an assistant to Alfred H. Swayne, a vice-president of General Motors, until Swayne's death in 1937, when Horner became Sloan's assistant.
		Horner's extensive research and interviews became the basis for written reports showing how motor transportation could be adapted to meet a company's particular needs.
		Horner was also active in promoting the use of bus transportation to and from railroad depots and air conditioning in railcars.
	www.loc.gov /rr/mss/text/horner.html (1817 words)

	[No title]
		Scheme, a mid-seventies' crossbreed of Lisp and Algol 60.
		Scheme, the language and the culture that goes with it, promises a mathematically more disciplined dynamism — but fails to deliver, to some extent.
		Scheme, by its spirit —to be grasped in the lambda experience or mystical onion— more than by its rudimentary definition, tends to separate these concerns, supporting arguably more intelligible layered architectures while retaining much of the power of Lisp.
	www.schnada.de /hylin/tao.html (2102 words)

	Sekino’s Fractal Gallery
		The coloring scheme (without limiting a number of colors), which is based on the "escape speed" of each sequence from a prescribed circle about the origin, is called the divergence scheme since all of the escaping sequences diverge to infinity.
		The divergence scheme leaves the Mandelbrot set with the canvas color since none of the parameters in the set are attached to the escaping sequences.
		The gatekeepers are painted by the convergence scheme with various shades of gold and the red background by the divergence scheme; thus, the Julia set in this pattern is depicted by the outlines of the gatekeepers.
	www.willamette.edu /~sekino/fractal/fractal.htm (2593 words)

	Springer Online Reference Works (via CobWeb/3.1 planetlab1.tamu.edu) (Site not responding. Last check: 2007-10-20)
		» Encyclopaedia of Mathematics »; H » Horner scheme
		At the beginning of the 19th century it was rediscovered, almost simultaneously, by W.G. Horner [1] and P.
		Horner's scheme is used for the efficient evaluation of polynomials.
	eom.springer.de.cob-web.org:8888 /H/h048030.htm (166 words)

	Horner's Method
		Randomness of Horner's rule and a new method of generating random numbers.
		Horner's rule and the computation of linear recurrences.
		An application of Horner's division scheme in the solution of algebriac congruences of higher degree.
	math.fullerton.edu /mathews/n2003/horner/HornerBib/Links/HornerBib_lnk_2.html (488 words)

	Horner - Wikipedia, the free encyclopedia
		Horner is an English surname that derives from the occupation horner who is a person who cuts the horns off of cattle, or deals in horns, or plays a horn.
		Johann Friedrich Horner (1831 - r 1886), an ophthalmologist, the namesake of the Horner's syndrome
		William George Horner (1786 - 1837) a British mathematician, the namesake of the Horner scheme
	en.wikipedia.org /wiki/Horner (166 words)

	Horner method [Archive] - Numerical Recipes Forum
		Sure, for some classes of polynomials Horner's can give demonstrably wrong examples, but for all the others, Horner is the most efficient and accurate way of evaluating a polynomial.
		The reason calculating sin() via its Taylor series is unstable is that the series is altenating, and that the absolute values of the terms are first increasing in magnitude before decaying slowly to zero.
		Thanx, Jan, your post is familiar for me :-) We have 4 methods of evaluating the polynome: sum forwards; backwards; substract the sum of all negative terms from the sum of all positive terms (which is the most unstable method); and Horner's scheme.
	www.nr.com /forum/archive/index.php/t-475.html (790 words)

	User documentation
		The famous Horner Scheme can be used to convert numbers between various numerical systems.
		This java application provides a way to learn and to practice converting numbers with the Horner Scheme.
		Now just push the Go button and according to your choices the Horner conversion table will be built on the right.
	www.htw-dresden.de /~paetzold/HornerExc/userdocu.htm (373 words)

	Polynomial (Site not responding. Last check: 2007-10-20)
		Which algorithm is used for a given polynomial depends on the form of the polynomial and the chosen x.
		To evaluate a polynomial in monomial form one can use the Horner scheme.
		The quotient can be computed using the Horner scheme.
	polynomial.kiwiki.homeip.net (1862 words)

	Polynomials
		Both expression are equal, but the latter form gives a more efficient way to evaluate the polynomial as the powers have disappeared.
		This function evaluates a polynomial given as a list of its coefficients, using the Horner scheme.
		The algorithm used to compute the series without first computing the individual polynomials is the Clenshaw-Smith recurrence scheme.
	yacas.sourceforge.net /refchapter10.html (1764 words)

	The list iterator and the Horner scheme
		(aux (cdr lst) (op acc (car lst))))) (aux lst acc)) (define (horner x lst)
		Hint : extend the Horner scheme when both arguments are lists of numbers
		(horner '(2 2 2) '(1 2 3)) =11
	members.aol.com /apicw/mw2/sch55.htm (59 words)

	IngentaConnect A Simple Test Qualifying the Accuracy of HornerS Rule for Polynom... (Site not responding. Last check: 2007-10-20)
		Whereas the accuracy of functions used by linear algebra have long been studied, little is available to decide on one scheme to evaluate polynomials.
		Common knowledge solely emphasizes that Horner's rule is a good scheme unless the indeterminate is close to one of the polynomial's roots.
		A result is defined to be faithful when it was correctly rounded whereas the rounding mode (up, down or to the nearest) cannot be known by users.
	www.ingentaconnect.com /content/klu/numa/2004/00000037/F0040001/05276602 (308 words)

	Scouts Nights Away Permit Scheme (Site not responding. Last check: 2007-10-20)
		The Horner Site is classified as a Green Field site under the terms of the Nights Away Permit Scheme.
		Horner is a Somerset County Scout Council Camping site.
		Those wishing to camp at Horner will have to supply details (probably a photocopy) of the Event Passport.
	www.hornermill.co.uk /nightsaway.html (102 words)

	Laboratoire de l'informatique du parallélisme
		Whereas the accuracy of the functions used by linear algebra have long been studied, little is available to decide on one scheme to evaluate a polynomial.
		The goal is to evaluate the performance of concurrent transfers (for example to improve collective communications) and not to discover the physical machines interconnection scheme (for administration purposes).
		In this report, we propose a multi-rate replicated scheme where some receivers (instead of the source) are designated to perform data replication for other receivers with lower capacity.
	www.ens-lyon.fr /LIP/Pub/rr2003.php (7666 words)

	Session 31
		We also talked about the use of Horner's scheme to determine the value of a number working from the left to the right rather than the right to the left like the previous technique uses (although this could be changed pretty easily).
		Put the previous values into notation using Horner's scheme.
		These previous techniques may seem a little trivial to you, because they simply take a number that you already know and convert it to that number that you already know.
	www.cs.uni.edu /~schafer/courses/080/sessions/s35.htm (464 words)

	Horner Downey & Co : Chartered Accountants and Registered Auditors (Site not responding. Last check: 2007-10-20)
		Horner Downey and Co Chartered Accountants and Registered Auditors
		Horner Downey are a long-standing firm of Chartered Accountants based in Bromborough.
		Horner Downey and Co is a member of the ICAEW Practice Assurance Scheme
	www.hornerdowney.com (92 words)

	chris horner - ResearchIndex document query (Site not responding. Last check: 2007-10-20)
		Horner Horner, H. And And Macgregor Macgregor, H. www.uoguelph.ca/~rgregory/Bodysize.pdf
		A first set of these methods are those proposed by Horner (1951)Miller et al.
		H X) respectively H 0)represents the Horner scheme H (respectively H 0)for the polynomial
	citeseer.ist.psu.edu /cis?q=Chris+Horner (537 words)

	Tests and Examples
		It is done by choosing an appropriate comparison scheme and then doing the comparison with the usual operators:
		versions in protected and unprotected mode produce the same result when Gauss scheme is used on an unstable matrix (in order to exercise rounding).
		horner.cpp is a really basic example of unprotecting the interval operations for a whole function (which computes the value of a polynomial by using Horner scheme).
	www.boost.org /libs/numeric/interval/doc/examples.htm (863 words)

	NVTS - Information for Those Interested in Applying to NVTS (via CobWeb/3.1 planetlab1.tamu.edu) (Site not responding. Last check: 2007-10-20)
		Phase 1 of the Northumbria Vocational Training Scheme aims to develop communication skills and self-awareness and encourages GP Registrars to develop their own continuing education.
		Phase 1 is a key stage in vocational training with the development of peer support through group work, which offers important preparation for future involvement in the primary health care team.
		We also encourage GP Registrars to identify and address their own learning needs by the timetabling of regular open sessions at which "hot topics" can be identified and dealt with.
	www.nvts.co.uk.cob-web.org:8888 /int_applying.asp?cont=structure (554 words)

	Modern Transport
		reflect Horner's original arrangement and are ordered sequentially by numbers assigned by him to each folder.
		also document Horner's involvement with various transportation committees, organizations, and conferences, many dealing with the much-debated issues of regulation and taxation.
		Horner, critique of paper on motor truck operation, n.d.
	memory.loc.gov /master/mss/eadxmlmss/2004/ms004015.xml (2879 words)

	lec11.html (Site not responding. Last check: 2007-10-20)
		This is an instance where Maple is careful to avoid expression swell.
		For univariate polynomials, to evaluate efficiently a dense polynomial, we may want to convert to a Horner form.
		Here the "optimized" codegeneration via repeated squaring does not produce an optimal way to evaluate.
	www.math.uic.edu /~jan/mcs320/Lec11/lec11.html (251 words)

	Horner Woods Scout Camp Site, Exmoor National Park, Somerset (Site not responding. Last check: 2007-10-20)
		The camp site is within the Exmoor National Park at Horner, a small hamlet of some nine
		The fields are on the banks of the Horner Water, a river running through the site.
		Overnight stops are payable at Horner Mill (see map).
	www.hornermill.co.uk /scoutcampsite.html (283 words)

	Polynomial - Wikipedia, the free encyclopedia (via CobWeb/3.1 planetlab1.tamu.edu) (Site not responding. Last check: 2007-10-20)
		A polynomial equation is an equation in the form of a polynomial equal to zero or equal to another polynomial.
		All the other functions that computers need to evaluate, such as trigonometric functions, logarithms and exponential functions, must then be approximated in software by suitable piecewise rational functions.
		One can then show that "every zero gives rise to a linear factor", or more formally: if f is a polynomial in R[X] and r is an element of R such that f(r) = 0, then the polynomial (X − r) divides f.
	en.wikipedia.org.cob-web.org:8888 /wiki/Polynomials (2700 words)

	Numerical analysis (Site not responding. Last check: 2007-10-20)
		One of the simplest problems is the evaluation of a function at a given point.
		But even evaluating a polynomial is not straightforward: the Horner scheme is often more efficient than the obvious method.
		Generally, it is important to estimate and control round-off errors arising from the use of floating point arithmetic.
	numerical-analysis.kiwiki.homeip.net (1581 words)

	Fortran90 - Appendix 11
		There are no errors in the numerical algorithm (Horner's scheme) or in the comments in the program.
		But some programming errors are included in the presented program, several of these are based on a mixture of Fortran and Pascal.
		At the the specification of the array to store the matrix, you may chose either the method in a) or b) above, or perhaps invent a third method.
	www.whoi.edu /CIS/training/classes/f77to90/a11.html (3642 words)

	RR-4707 : A simple test qualifying the accuracy of Horner's rule for polynomials
		RR-4707 - A simple test qualifying the accuracy of Horner's rule for polynomials
		Abstract : Polynomials are used in many applications and hidden in libraries such as libm.
		La culture commune reconnaît seulement que l'évaluation de Horner se comporte bien à moins que l'indéterminée ne soit proche d'une des racines du polynôme. Nous proposons ici un critère de fidélité pour une étape du schéma de Horner.
	www.inria.fr /rrrt/rr-4707.html (452 words)

	Constrained, non-linear, derivative-free parallel optimization of continuous, high computing load, noisy objective ... (Site not responding. Last check: 2007-10-20)
		The ``inverse lexical order'' is easier to transform in a multivariate horner scheme.
		You can see that we retrieve inside this decomposition of the algorithm for the evaluation of the polynomial
		We can now define an algorithm which computes the value of a multivariate polynomial ordered by degree by multivariate horner scheme:
	www.applied-mathematics.net.cob-web.org:8888 /mythesis/node16.html (464 words)

	Horner's Method (Site not responding. Last check: 2007-10-20)
		Dept., Arizona State Univ., Tucson, AZ Example of Horner's Scheme
		Horner's Rule for a Polynomial and Its Derivative
		Dept., University of Colorado, Boulder, CO Newton's Method with Horner's Method PDF
	math.fullerton.edu /mathews/n2003/horner/HornerBib/Links/HornerBib_lnk_1.html (129 words)

	Polynomials (Site not responding. Last check: 2007-10-20)
		It can evaluate a polynomial with Horner's scheme
		Of course, it is slower that Horner's scheme.
		The polynomials need not have the same degree.
	mathsrv.ku-eichstaett.de /MGF/homes/grothman/euler/polynomials.html (267 words)

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