In numerical analysis, Laguerre's method is a root-finding algorithm tailored to polynomials. In other words, Laguerre's method can be used to numerically...

analysis. He also investigated orthogonal polynomials (see Laguerre polynomials). Laguerre's method is a root-finding algorithm tailored to polynomials. He...

theorem Laguerre's method Methods of computing square roots Newton's method in optimization Richardson extrapolation Root-finding algorithm Secant method Steffensen's...

In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are nontrivial solutions of Laguerre's differential equation: x y ″...

starting point of Horner's method for computing the roots. Closely related to Newton's method are Halley's method and Laguerre's method. Both use the polynomial...

Jenkins–Traub algorithm — fast, reliable, and widely used Laguerre's method Splitting circle method Analysis: Wilkinson's polynomial Numerical continuation...

114–139, doi:10.1016/j.laa.2005.06.022 Li, T. Y.; Zeng, Zhonggang (1992), "Laguerre's Iteration In Solving The Symmetric Tridiagonal Eigenproblem - Revisited"...

analysis Gauss–Laguerre quadrature (named after Carl Friedrich Gauss and Edmond Laguerre) is an extension of the Gaussian quadrature method for approximating...

In mathematics, the Runge–Kutta–Fehlberg method (or Fehlberg method) is an algorithm in numerical analysis for the numerical solution of ordinary differential...

Transform based on Laguerre function expansion. The Laguerre method can be used to simulate a weakly nonlinear circuit and the Laguerre method can invert a...

stage takes these potential zeros and “polishes” them by applying Laguerre's method to bring them close to the actual zeros of the polynomial. The third...

{\displaystyle \ s\ ,} using a root-finding algorithm such as Newton's method or Laguerre's method for a given time   t     . {\displaystyle \ t\ ~.} The value...

1007/BF02165404. S2CID 122353612. Bunch, J. R.; Parlett, B. N. (1971). "Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations". SIAM Journal...

functions belonging to the Laguerre–Pólya class" Archived 2008-10-06 at the Wayback Machine by D. Dryanov and Q. I. Rahman, Methods and Applications of Analysis...

The Fokas method, or unified transform, is an algorithmic procedure for analysing boundary value problems for linear partial differential equations and...

(1881) pointed out that Laguerre's geometry is indeed a special case of Lie's sphere geometry. He also represented Laguerre's oriented spheres by quaternions...

integrals on the whole real line and Gauss-Laguerre quadrature for integrals on the positive reals. Monte Carlo methods can also be used, or a change of variables...

Synthesis of electrical networks by means of the Fourier transforms of Laguerre's functions (Unpublished doctoral dissertation). Massachusetts Institute...

minimizing the power is constant. More generally, French mathematician Edmond Laguerre defined the power of a point with respect to any algebraic curve in a similar...

evaluate. The "Free Parameter" method is another method (called "snake oil" by H. Wilf) to evaluate these sums. Both methods discussed so far have n as limit...

PMC 11196076. PMID 38904978. Hu X, Laguerre V, Packert D, Nakasone A, Moscinski L (2015). "A Simple and Efficient Method for Preparing Cell Slides and Staining...

deconvolution based methods but they suffer from truncation and sampling problems. Moreover, application of methods like Laguerre gauss expansion is mathematically...

{\displaystyle H=\sinh ^{-1}\left({\frac {H+M}{e}}\right)} . This method is related to the Newton's method solution above in that E n + 1 = E n − E n − e sin ⁡ (...

usually called "ensembles"), or Wishart–Laguerre ensemble (since its eigenvalue distribution involve Laguerre polynomials), or LOE, LUE, LSE (in analogy...

) d x . {\displaystyle \langle f,g\rangle =\int w(x)f(x)g(x)\,dx.} For Laguerre polynomials on ( 0 , ∞ ) {\displaystyle (0,\infty )} the weight function...

{1}{t-x+u}}\\&=e^{x^{2}}\,e^{-(x-u)^{2}}\\&=e^{2xu-u^{2}}\end{aligned}}} For associated Laguerre polynomials, L n ( α ) ( x ) = x − α e x n ! d n d x n ( e − x x n + α...

Blossom (functional) Root of a function nth root (radical) Surd Square root Methods of computing square roots Cube root Root of unity Constructible number...

,} where Ln are the Laguerre polynomials. This example illustrates how the Hermite and Laguerre polynomials are linked through the Wigner...

Mathematical Methods in the Physical Sciences is a 1966 textbook by mathematician Mary L. Boas intended to develop skills in mathematical problem solving...

{1-x^{2}}}} . One may also want to integrate over semi-infinite (Gauss–Laguerre quadrature) and infinite intervals (Gauss–Hermite quadrature). It can be...