Root finding algorithm

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	Root-finding algorithm - Wikipedia, the free encyclopedia
		The simplest root-finding algorithm is the bisection method: we start with two points a and b which bracket a root, and at every iteration, we pick either the subinterval [a, c] or [c, b], where c = (a + b) / 2 is the midpoint between a and b.
		A root-finding algorithm is a numerical method or algorithm for finding a value x such that f(x) = 0, for a given function f.
		The bisection method is guaranteed to converge to a root, however, its progress is rather slow (the rate of convergence is linear).
	www.wikipedia.org /wiki/Root-finding_algorithm (765 words)

	Numerical Root Finding
		However, since the secant method does not always bracket the root, the algorithm may not converge for functions that are not sufficiently smooth.
		The emphasis on bracketing the root may sometimes restrict the false position method in difficult situations while solving highly nonlinear equations.
		The false position method, which sometimes keeps an older reference point to maintain an opposite sign bracket around the root, has a lower and uncertain convergence rate compared to the secant method.
	www.efunda.com /math/num_rootfinding/num_rootfinding.cfm (482 words)

	Computers, Algorithms
		Root-finding algorithm A root-finding algorithm is a numerical method or algorithm for finding a value ''x'' such...
		Flooding algorithm A flooding algorithm is an algorithm for distributing material to every part of a connect...
		Stony Brook Algorithm Repository This is a collection of implementations for 75 fundamental algorithms problems, including data structures, numerical and combinatorial algorithms,graph algorithms, and computational geometry.
	www.serebella.com /directory/Computers/Algorithms/Pseudorandom (772 words)

	Finding Soulmate
		Floyd's cycle-finding algorithm finds such an equality by running two i 27: The best way to visualize this alg 31: ng discrete logarithm s based on Floyd's cycle-finding algorithm.
		Floyd's cycle-finding algorithm 1: Floyd's cycle-finding algorithm is an algorithm which can detect 21: u;, a multiple of the cycle length.
		Direction finding 1: '''Direction finding ''' (DF) refers to the establishment of the direct 3: Direction finding requires an antenna (electronics)antenna tha 7: are generally used for highly accurate direction finding such as that used in signals intelligence (SI Finding Neverland 1: The movie poster for ''Finding Neverland''.
	www.elusiveeye.com /side5928-finding-soulmate.html (575 words)

	GNU Scientific Library -- Reference Manual - One dimensional Root-Finding
		Algorithms which proceed by bracketing a root are guaranteed to converge.
		While it is not absolutely required that f have a root within the search region, numerical root finding functions should not be used haphazardly to check for the existence of roots.
		For these algorithms the initial interval must contain a zero-crossing, where the function is negative at one end of the interval and positive at the other end.
	panoramix.ift.uni.wroc.pl /knowledge/gsl-ref/gsl-ref_30.html (2648 words)

	Lecture Notes: Root Finding
		Other methods such as spline interpolation are sometimes used for root finding; the basic idea (fitting a polynomial and using the root of the polynomial as the next estimate) remains the same.
		Finding roots in multiple dimensions can be much more difficult.
		But of course, if we knew where the "real" root was we wouldn't have to do this; therefore we settle for something in the approximate area.
	www.cstp.umkc.edu /public/courses/ece216/f02/rootfinding.html (1691 words)

	Programmer's toolbox: A root-finding algorithm
		The algorithm maintains two points that straddle the root (meaning that the signs of ƒ(x) are different).
		This is precisely why the algorithm tends to dive for the root so aggressively once it gets close to it.
		In the original IBM algorithm, as with my earlier translations, that test is an absolute one, testing the value of the range, x2-x1.
	www.eetasia.com /ARTICLES/2005AUG/C/2005AUG_PTB_WK2.HTM (3107 words)

	Polynomial Root-Finding : Analysis and Computational Investigation of a Parallel Algorithm - NARENDRAN, TIWARI (ResearchIndex)
		On the Convergence of a Parallel Algorithm for Finding..
		Abstract: A practical version of a parallel algorithm that approximates the roots of a polynomial whose roots are all real is developed using the ideas of an existing NC algorithm.
		A particular implementation of the algorithm that performs well in practice is described and its run-time behaviour is compared with the analytical predictions.
	citeseer.lcs.mit.edu /narendran92polynomial.html (493 words)

	CSC Poster: roots.html
		Root finding is a fundamental operation in many computer graphics algorithms, most prominently ray/surface intersection in ray tracing.
		When some properties of a function are known, such as its regions of monotonicity, then a robust scalar root-finding algorithm such as reguli-falsi can be used, perhaps in conjunction with bracketed Newton steps.
		In this talk I will present the techniques of interval analysis, automatic differentiation, and the Newton interval root-finding algorithm as applied to ray-traced rendering.
	www.csclub.uwaterloo.ca /old/events/roots.shtml (208 words)

	GNU Scientific Library -- Reference Manual: Algorithms without Derivatives
		This is a version of the Hybrid algorithm which replaces calls to the Jacobian function by its finite difference approximation.
		The Broyden algorithm is a version of the discrete Newton algorithm which attempts to avoids the expensive update of the Jacobian matrix on each iteration.
		The algorithm may become unstable if the finite differences are not a good approximation to the true derivatives.
	linux.duke.edu /~mstenner/free-docs/gsl-ref-1.0/gsl-ref_427.html (333 words)

	Efficient Root-Finding Algorithm with Application to List Decoding of Algebraic-Geometric Codes - Wu, Siegel (ResearchIndex)
		Abstract: A list decoding for an error-correcting code is a decoding algorithm that generates a list of codewords within a Hamming distance t from the received vector, where t can be greater than the error-correction bound.
		8 Computing roots of polynomials over function fields of curve..
		Fast interpolation and factorization algorithms have been studied in
	citeseer.ist.psu.edu /476355.html (582 words)

	Root Finding - GIDForums
		Bisection method for finding a real root of a continuous function:
		You have to note intervals where you think roots are to be found
		I also find that recursive programs are often difficult to debug, whereas with a loop, you can simply put a few printf()'s here and there and know exactly how you got there and where you are going.
	www.gidforums.com /t-3989.html (819 words)

	Polynomial root finding: A statistical study of a bisection-exclusion algorithm
		Polynomial root finding: A statistical study of a bisection-exclusion algorithm
		This algorithm belongs to the class of exclusion methods : it searches a specified bounded domain E containing the roots of f, removes from E subsets which do not contain any root and returns an arbitrarily small subset of E containing all the roots.
		Such an algorithm depends mainly on two ingredients : the choice of an exclusion test and a strategy for its implementation.
	mip.ups-tlse.fr /publi/rappLAO/95.04.html (153 words)

	7.2.2 Newton's Method and the Secant Method
		Perhaps the best known root finding algorithm is Newton's method (a.k.a.
		The bisection method is a very intuitive method for finding a root but there are other ways that are more efficient (find the root in fewer iterations).
		So it is a good idea to limit the number of iterations allowed by your program to prevent the algorithm from iterating forever without success.
	www.physics.nau.edu /~hart/matlab/node52.html (597 words)

	finding : Encyclopedia Articles
		Gene finding is the area of computational biology that is concerned with algorithmically identifying stretches of...
		This is a comprehensive resource for finding information about plants in the United States...
		Social studies department uses this site a lot, but I think world language could make use of it as well to do country fact finding.
	www.logicjungle.com /wikifind-finding.html (134 words)

	R: An implementation of the bisection algorithm for root finding.
		R: An implementation of the bisection algorithm for root finding.
		An implementation of the bisection algorithm for root finding.
		Since the quantities involved are generally restricted to a subset of [0,1] we use bisection to find the roots.
	www.maths.lth.se /help/R/.R/library/Icens/html/Bisect.html (81 words)

	16.htm
		Renegar, On the complexity of a piece-wise linear algorithm for approximating roots of complex polynomials, Math.
		C.A. Neff, Specified precision polynomial root isolation is in NC, in: Proc.
		Smale, On the topology of algorithms I, Complexity 3 (1987) 81--89.
	www.elsevier.com /homepage/sac/cam/mcnamee/16.htm (1800 words)

	mn200035.htm
		Whilst we do normally have the open-loop poles (because we’ve obtained them from the model), when we close the loop the denominator of the C.L.T.F. is no longer in factored form and we would need a root finding algorithm to determine the C.L. poles.
		Root finding is not straight forward for systems of order greater than two.
		The Routh-Hurwitz stability criterion is based on a method, which we will call the Routh-Hurwitz method, that determines the number of closed loop poles with positive real parts for any order of system.
	www.brunel.ac.uk /~emstrsp/mn2007.i2h/mn200035.htm (821 words)

	The Ultimate Wilkinson's polynomial - American History Information Guide and Reference
		A small change in one coefficient can lead to drastic changes in the roots found by root-finding algorithms.
		The problem of finding the roots is ill-conditioned.
		Wilkinson's polynomial of degree 20 has 20 roots, but, as the graph below shows, the function becomes almost horizontal near the x-axis.
	www.historymania.com /american_history/Wilkinson%27s_polynomial (99 words)

	Embedded.com - A root finder's roots
		For the sake of completeness, I should mention that finding the root at which f(x) = 0 is equivalent to finding the value of x for any specified y, since we can always transform one problem into the other simply by adding an offset to y.
		When you consider that I've been using the algorithm for no less than 34 years and that it had a long and honorable history before that, you'll appreciate this as a rather remarkable finding.
		Since the root finder has to deal with arbitrary functions, it stands to reason that some functions are going to like the fit of vertical parabolas, others horizontal ones.
	www.embedded.com /story/OEG20030508S0030 (3254 words)

	Bisection
		In numerical analysis, bisection is a root-finding algorithm which works by dividing an interval in half, and then selecting the interval in which the root exists.
		If we had been told that the "hen's egg," when be conclusive, since the KOH-I-NUR was certainly uncut in.
	www.termsdefined.net /bi/bisection.html (347 words)

	Citations: A root-finding algorithm based on Newton's method - Madsen (ResearchIndex)
		Citations: A root-finding algorithm based on Newton's method - Madsen (ResearchIndex)
		1977, Foster 1981] and the randomized Jenkins Traub algorithm [Jenkins and Traub 1970] all three for approximating a single zero z of p(x) which can be extended to approximating other zeros by means of deflation of the input polynomial via its numerical.
		of such algorithms, the practical heuristic champions in efficiency (in terms of computer time and memory space used, according to the results of many experiments) are various modifications of Newton s iteration, z(i 1) z(i) Gamma a(i)p(z(i) p 0 (z(i) a(i) being the step size parameter
	citeseer.ist.psu.edu /context/558252/0 (415 words)

	pubs.html
		Fortune, Convergence analysis of an iterated-eigenvalue polynomial root-finding algorithm, submitted.
		Fortune, An iterated eigenvalue algorithm for approximating the roots of univariate polynomials, submitted.
		Fortune, Algorithms for the prediction of indoor radio propagation, manuscript, 1998.
	cm.bell-labs.com /who/sjf/pubs.html (413 words)

	RootFinding.java
		Must be initialized by initAll() / Poly2_nMax[] square = new Poly2_nMax[HFE2_n.extensionDegree+1]; /* registers for root finding algorithm.
		The algorithm used in this class is described in
		This class computes root for a given polynomial over GF(2^n).
	www.esat.kuleuven.ac.be /~cwolf/hfe_kg/source/RootFinding.java (531 words)

	On Representations of Algebraic-Geometric Codes for List Decoding (ResearchIndex)
		We do this by presenting a root-finding algorithm for univariate polynomials over function fields when their coefficients lie in finite-dimensional linear spaces, and proving that there is a polynomial size representation given which the root finding algorithm runs in polynomial time.
		Abstract: We show that all algebraic-geometric codes possess a succinct representation that allows for the list decoding algorithms of [15, 7] to run in polynomial time.
		8 Computing roots of polynomials over function fields of curve..
	citeseer.ist.psu.edu /473056.html (418 words)

	Computation of Varieties
		may be given (see the Roots intrinsic function in the Real and Complex Fields chapter (Chapter REAL AND COMPLEX FIELDS)).
		may be given (see the Roots function in the Real and Complex Fields chapter (Chapter REAL AND COMPLEX FIELDS)).
		If K is not a finite field then the ideal must be the full polynomial ring or be zero-dimensional so that the variety is known to be finite.
	www.math.lsu.edu /magma/text1115.htm (327 words)

	CATAPULT_6_14_2.html
		We use our contour plot to obtain an initial starting point for our root finding algorithm.
		We proceed to optimize this function of two variables a and theta, using the calculus approach of setting the respective partial derivatives with respect to a and theta equal to 0 and solving for values of a and theta which make these partial derivatives equal to 0.
	www.rose-hulman.edu /Class/CalculusProbs/Problems/CATAPULT/CATAPULT_6_14_2.html (79 words)

	Interval Methods Revisited - Van Hentenryck, McAllester, Kapur (ResearchIndex)
		Our findings show that fairly straightforward refinements of interval methods inspired by AI constraint propagation techniques result in a multivariate root finding algorithm that is competitive with continuation methods on most benchmarks and which can solve a variety of systems that are totally infeasible for continuation methods.
		Abstract: This paper presents a branch and cut algorithm to find all isolated solutions of a system of polynomial constraints.
		2 Overview of The Approach As mentioned, Newton is a global search algorithm which solves a problem by dividing it into subproblems...
	citeseer.lcs.mit.edu /vanhentenryck95interval.html (556 words)

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		Custom Algorithm development using the SciCode ™ process,
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