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Graeffe's method – Algorithm for finding polynomial roots; Lill's method – Graphical method for the real roots of a polynomial; MPSolve – Software for approximating the roots of a polynomial with arbitrarily high precision; Multiplicity (mathematics) – Number of times an object must be counted for making true a general formula
The Coppersmith method, proposed by Don Coppersmith, is a method to find small integer zeroes of univariate or bivariate polynomials, or small zeros modulo a given integer. The method uses the Lenstra–Lenstra–Lovász lattice basis reduction algorithm (LLL) to find a polynomial that has the same zeroes as the target polynomial but smaller ...
In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method, so it is considered a quasi-Newton method. Historically, it is as an evolution of the ...
An illustration of Newton's method. In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function.
Edmond Halley was an English mathematician and astronomer who introduced the method now called by his name. The algorithm is second in the class of Householder's methods, after Newton's method. Like the latter, it iteratively produces a sequence of approximations to the root; their rate of convergence to the root is cubic. Multidimensional ...
The simplest form of the formula for Steffensen's method occurs when it is used to find a zero of a real function; that is, to find the real value that satisfies () =.Near the solution , the derivative of the function, ′, is supposed to approximately satisfy < ′ <; this condition ensures that is an adequate correction-function for , for finding its own solution, although it is not required ...
Square roots and other roots: Integer square root; Methods of computing square roots; nth root algorithm; hypot — the function (x 2 + y 2) 1/2; Alpha max plus beta min algorithm — approximates hypot(x,y) Fast inverse square root — calculates 1 / √ x using details of the IEEE floating-point system
Laguerre's method may even converge to a complex root of the polynomial, because the radicand of the square root may be of a negative number, in the formula for the correction, , given above – manageable so long as complex numbers can be conveniently accommodated for the calculation. This may be considered an advantage or a liability ...