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	Laguerre's method - Wikipedia, the free encyclopedia
		In numerical analysis, Laguerre's method is a root-finding algorithm tailored to polynomials.
		This means that Laguerre's method converges even faster than Newton's method.
		Laguerre's method also works for polynomials with real coefficients that have complex roots.
	en.wikipedia.org /wiki/Laguerre's_method (268 words)

	Laguerre's method -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-05)
		In (Click link for more info and facts about numerical analysis) numerical analysis, Laguerre's method is a (Click link for more info and facts about root-finding algorithm) root-finding algorithm tailored to (A mathematical expression that is the sum of a number of terms) polynomials.
		Laguerre's method tries to improve this approximation (Click link for more info and facts about iteratively) iteratively by using the (Click link for more info and facts about recurrence relation) recurrence relation
		This means that Laguerre's method converges even faster than (Click link for more info and facts about Newton's method) Newton's method.
	www.absoluteastronomy.com /encyclopedia/l/la/laguerres_method.htm (312 words)

	Encyclopedia: Laguerre's method
		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.
		Laguerre's method tries to improve this approximation iteratively by using the recurrence relation An iterative method attempts to solve a problem (for example an equation or system of equations) by finding successive approximations to the solution starting from an initial guess.
		In numerical analysis, Newtons method (or the Newton-Raphson method) is an efficient algorithm for finding approximations to the zeros (or roots) of a real-valued function.
	www.nationmaster.com /encyclopedia/Laguerre%27s-method (465 words)

	Abstract (Site not responding. Last check: 2007-11-05)
		The paper presents an efficient algorithm, based on the application of the spectral Laguerre method for approximation of temporal derivatives as applied to the problem of seismic wave propagation in the heterogeneous viscoelastic medium.
		This approach is an analogue to the frequency-domain forward modeling, where instead of the frequency w we have number m- the degree of the Laguerre polynomials.
		Application of the Laguerre transform together with finite differences along the spatial coordinates reduces the solution of the original problem to a system of linear algebraic equations with a sparse matrix, independent of number m.
	www.ig.cas.cz /activities/konyuk.htm (275 words)

	SINUM Volume 18 Issue 6
		Laguerre’s method is an efficient and reliable method for finding zeros of polynomials and certain other functions.
		A new derivation and motivation of Laguerre’s method is given, which allows it to be included in a class of methods as general as methods of order three or more based on direct generalized Hermite or hyperosculatory interpolation.
		Methods of order 4 and 3.303 are investigated and numerical results indicate that for large $(100 \times 100)$ eigenvalue problems the method of order 3.303 is as efficient and reliable as Laguerre’s method.
	locus.siam.org /SINUM/volume-18/art_0718069.html (173 words)

	Universal Dynamics - Engineering, Software and Productivity (Site not responding. Last check: 2007-11-05)
		The Laguerre functions used in DMT are well suited to modeling the types of transient signals found in process control because Laguerre functions have similar behavior to the processes being modeled.
		As with Fourier series, the DMT modeling method produces a set of weights for the Laguerre functions in the series such that when the weighted functions are summed a reasonable approximation of the original transient signal is obtained.
		The DMT modeling method was found to be particularly useful for the identification of the unusual transient response of steam temperature during MW load changes.
	udl.com /library/p86.html (2216 words)

	List of numerical analysis topics - Wikipedia, the free encyclopedia
		Galerkin method — a finite element method in which the residual is orthogonal to the finite element space
		Boundary element method — based on transforming the PDE to an integral equation on the boundary of the domain
		Analytic element method — similar to the boundary element method, but the integral equation is evaluated analytically
	en.wikipedia.org /wiki/List_of_numerical_analysis_topics (489 words)

	Electronic Journal of Theoretical Physics (EJTP)
		A method of estimating the maximum possible atomic number (i.e., Z value) that can be possessed by relatively stable superheavy elements (SHEs) has been proposed in this paper.
		This method is based upon the supposition that no electron orbiting a SHE atomic nucleus can have a speed equal to, or greater than, 0.92c (where c is the speed of light) without significantly increasing the probability of electron capture by that atomic nucleus.
		Method of the solution of the main problem of homogeneous spaces thermodynamics for non-compact spaces in the case of non-compact Lie groups is presented in the article.
	www.ejtp.com /articles (2593 words)

	Polynomial - Open Encyclopedia (Site not responding. Last check: 2007-11-05)
		The Difference Engine of Charles Babbage was designed to create large tables of values of logarithms and trigonometric functions automatically by evaluating approximating polynomials at many points using Newton's difference method.
		As there is generally no closed formula to calculate the roots of a polynomial of degree 5 and higher root-finding algorithm are studied in numerical analysis to approximate the roots.
		Approximations for the real roots of a given polynomial can be found using Newton's method, or more efficiently using Laguerre's method which employs complex arithmetic and can locate all complex roots.
	open-encyclopedia.com /Polynomial (1761 words)

	Laguerre's Iteration In Solving The Symmetric Tridiagonal Eigenproblem - Revisited - Li, Zeng (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		The method directly evaluates eigenvalues and uses inverse iteration as an option when eigenvectors are needed.
		Laguerre's iteration in solving the symmetric tridiagonal eigenproblem - a revisit.
		56 A divide and conquer method for the symmetric tridiagonal ei..
	citeseer.ist.psu.edu /li92laguerres.html (640 words)

	Laguere - TX00. Jowel Laguere, Ph.D. TX00. Jowel Laguere. Vice President. (Site not responding. Last check: 2007-11-05)
		Biography of Edmond Laguerre (1834-1886) Edmond Laguerre had poor health as a boy and this impeded his studies lines in the complex projective plane.
		Laguerre graduated from the École Polytechnique in 1854 and decided.
		Laguerre Polynomial -- from MathWorld Laguerre Polynomial -- from MathWorld The Laguerre polynomials are solutions L_n(x) to the Laguerre differential equation with nu=0.
	www.destarter.com /Laguerre/Laguere.html (505 words)

	On The Laguerre Method For Numerically Inverting Laplace Transforms - Abate, Choudhury, Whitt (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		On The Laguerre Method For Numerically Inverting Laplace Transforms (1996)
		Abate, J., Choudhury, G. and Whitt, W. On the Laguerre method for numerically inverting Laplace transforms.
		60 The Fourier-series method for inverting transforms of probab..
	citeseer.ist.psu.edu /abate96laguerre.html (939 words)

	Results of Flux Calculations (Site not responding. Last check: 2007-11-05)
		After solving the adjoint radiative transfer equation, the radiative fluxes at each level can be derived by integrating the "contributions" of all the layers (referring to equation 5.21).
		As the adjoint mean intensity does not change with optical thickness linearly, we use the Gauss-Laguerre method for the numerical integrations.
		Figure 5.2 compares the fluxes computed from the adjoint method and fluxes computed from the forward method.
	asd-www.larc.nasa.gov /~yhu/paper/thesisall/node47.html (129 words)

	Laguerre's Method Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-11-05)
		Looking For laguerre's method - Find laguerre's method and more at Lycos Search.
		Find laguerre's method - Your relevant result is a click away!
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	www.karr.net /search/encyclopedia/Laguerre%27s_method (446 words)

	Laguerre's Method (Site not responding. Last check: 2007-11-05)
		Laguerre-like methods for the simultaneous approximation of polynomial zeros.
		Improving Laguerre's method to cope with symmetry pitfalls in polynomial root-finding.
		Laguerre's iteration and the method of traces for eigenproblems.
	mathews.ecs.fullerton.edu /n2003/laguerresethod/LaguerreMethodBib/Links/LaguerreMethodBib_lnk_2.html (358 words)

	Complex Roots: Laguerre’s Method (Site not responding. Last check: 2007-11-05)
		The beauty of Muller’s Method is it will work for a general function f(x).
		The most common method of achieving this is called Laguerre’s Method.
		Laguerre’s Method is a sure-fire way of finding one, perhaps complex, root of a polynomial.
	eyrie.shef.ac.uk /lec2/sld009.html (186 words)

	Polynomial (Site not responding. Last check: 2007-11-05)
		In order to determine function values of polynomials for given values of the variable x, one does not apply the polynomial as a formula directly, but uses the much more efficient Horner scheme instead.
		If the evaluation of a polynomial at many equidistant points is required, Newton's difference method reduces the amount of work dramatically.
		If however the set of allowed candidates is expanded to the complex numbers, every (non-constant) polynomial has a root (see Fundamental Theorem of Algebra).
	www.sciencedaily.com /encyclopedia/polynomial (1567 words)

	CPC Licence Alert (Site not responding. Last check: 2007-11-05)
		This program solves the QCD evolution integrodifferential equation (the Altarelli-Parisi equation) satisfied by quark or gluon distribution functions such as are measured in deep inelastic scattering.
		The Altarelli-Parisi equations are transformed into a form suitable for orthogonal polynomial methods.
		The relevant orthonormal polynomials are the Laguerre polynomials.
	www.cpc.cs.qub.ac.uk /summaries/ACGR.html (194 words)

	The Mathematical Institute Eprints Archive - Iterative methods for roots of polynomials
		Mekwi, W.R. Iterative methods for roots of polynomials.
		We describe iterative methods for polynomial zero finding and, specifically, the Laguerre method and how it is used in the NAG subroutine C02AFF.
		In chapter three, we look at the Laguerre method as used in C02AFF in further detail, describe the behaviour of the bug and how the problem has been solved.
	eprints.maths.ox.ac.uk /archive/00000016 (175 words)

	Engineering and Scientific Subroutine Library for AIX Version 3 Release 3: Guide and Reference - SGLGQ and ...
		These functions approximate the integral of a real valued function over a semi-infinite interval, using the Gauss-Laguerre Quadrature method of specified order.
		is the order of the quadrature method to be used.
		The integral is approximated for a real valued function over a semi-infinite interval, using the Gauss-Laguerre Quadrature method of specified order.
	www.ncsa.uiuc.edu /UserInfo/Resources/Hardware/IBMp690/IBM/usr/lpp/essl.html.en_US/html/essl254.html (435 words)

	ROOT - Interactive rootfinding (Site not responding. Last check: 2007-11-05)
		ROOT is a simple interactive program that allows you to set up a scalar nonlinear equation, an error tolerance, a function F(X), and some starting values, and then apply one of a number of methods for seeking a root of the equation F(X) = 0.
		FIXED implements the fixed point method for a nonlinear equation.
		HALLEY implements Halley's method for a nonlinear equation.
	orion.math.iastate.edu /burkardt/f_src/root/root.html (265 words)

	Mathematics of Computation
		J. Boyd, Spectral methods using rational basis function in an infinite interval, J.
		Guo Ben-yu and Jie Shen, Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval, Numer.
		Xu Cheng-long and Guo Ben-yu, Laguerre pseudospectral method for nonlinear partial differential equations, J.
	www.ams.org /mcom/2004-73-245/S0025-5718-03-01521-7/home.html (508 words)

	Complex Roots: Laguerre’s Method (Site not responding. Last check: 2007-11-05)
		FORTRAN will do complex arithmetic for you, but it is rather complicated to describe.
		In common with this method, once a root is found, the order of the polynomial is reduced by synthetic division, and the roots of the remainder polynomial are found.
		approximate roots, polishes off all n roots with Laguerre’s method.
	eyrie.shef.ac.uk /will/lec2/sld009.html (186 words)

	An Improved Laguerre Eigensolver for Unsymmetric Matrices
		A Laguerre iteration procedure is described for finding the eigenvalues of unsymmetric matrices with improved efficiency.
		Compared to the QR method, the processing time for dense matrices is reduced by roughly a factor of 1.6 and for sparse matrices by a factor of up to 2.8 without sacrificing accuracy.
		Alternatively, the Laguerre procedure will typically provide one additional significant digit, compared to the QR method, when allowed to run for as long as the QR method.
	epubs.siam.org /sam-bin/dbq/article/34963 (142 words)

	Laguerre-Galerkin Method for Nonlinear Partial Differential Equations on a Semi-Infinite Interval (Site not responding. Last check: 2007-11-05)
		Laguerre-Galerkin Method for Nonlinear Partial Differential Equations on a Semi-Infinite Interval
		A Laguerre-Galerkin method is proposed and analyzed for the Burgers equation and Benjamin-Bona-Mahony (BBM) equation on a semi-infinite interval.
		By reformulating these equations with suitable functional transforms, it is shown that the Laguerre-Galerkin approximations are convergent on a semi-infinite interval with spectral accuracy.
	www.math.psu.edu /ccma/Reports/Publications/Publications1999/Info_files/AM210.html (96 words)

	The Orthogonal QD-Algorithm - Von Matt (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		A generalization of the Givens transformation is also introduced, which has applications besides the orthogonal qd-algorithm.
		The shift strategy of the orthogonal qd-algorithm is based on Laguerre's method, which is used to compute...
		7 The Laguerre iteration in solving the symmetric tridiagonal..
	citeseer.ist.psu.edu /vonmatt94orthogonal.html (563 words)

	IngentaConnect Transient radiative heat transfer through thin films using Laguer... (Site not responding. Last check: 2007-11-05)
		Heat transfer through a semiconductor or dielectric thin film is investigated by using the single relaxation time approximation to the Boltzmann equation.
		The radiance is expanded in terms of the Laguerre polynomial with time as argument, and the ensuing time-independent equation is solved with the aid of the Galerkin technique.
		Films of different thicknesses, ranging from 0.01 to 10 mean free paths, have been considered.
	api.ingentaconnect.com /content/iop/jphysd/2003/00000036/00000023/art00023 (216 words)

	XploRe Help: Function Index (Site not responding. Last check: 2007-11-05)
		Berndt-Hall-Hall-Hausman method to find a minimum of a given negative log-likelihood function (and maximum of the corresponding likelihood function).
		Brent's method for the minimization of a given scalar function using derivatives
		implements Laguerre's method for improving a given complex value until it converges to a root of a given polynomial
	www.xplore-stat.de /help/0nummath.html (624 words)

	Cerebral blood flow velocity response to induced and spontaneous sudden changes in arterial blood pressure -- Panerai ...
		Two different methods were used to estimate the linear dynamic relationship between MABP and MCBFV.
		decomposition was used to estimate the coefficients of the Laguerre
		obtained with the thigh cuff method in the same subjects.
	ajpheart.physiology.org /cgi/content/full/280/5/H2162 (7471 words)

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