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A few steps of the bisection method applied over the starting range [a 1;b 1].The bigger red dot is the root of the function. In mathematics, the bisection method is a root-finding method that applies to any continuous function for which one knows two values with opposite signs.
The bisection method has been generalized to higher dimensions; these methods are called generalized bisection methods. [3] [4] At each iteration, the domain is partitioned into two parts, and the algorithm decides - based on a small number of function evaluations - which of these two parts must contain a root. In one dimension, the criterion ...
The field of numerical analysis predates the invention of modern computers by many centuries. Linear interpolation was already in use more than 2000 years ago. Many great mathematicians of the past were preoccupied by numerical analysis, [5] as is obvious from the names of important algorithms like Newton's method, Lagrange interpolation polynomial, Gaussian elimination, or Euler's method.
In numerical analysis, Brent's method is a hybrid root-finding algorithm combining the bisection method, the secant method and inverse quadratic interpolation.It has the reliability of bisection but it can be as quick as some of the less-reliable methods.
Crank–Nicolson method (numerical analysis) D'Hondt method (voting systems) D21 – Janeček method (voting system) Discrete element method (numerical analysis) Domain decomposition method (numerical analysis) Epidemiological methods; Euler's forward method; Explicit and implicit methods (numerical analysis) Finite difference method (numerical ...
The bisection method based on Descartes' rules of signs and Vincent's auxiliary theorem has been introduced in 1976 by Akritas and Collins under the name of Modified Uspensky algorithm, [3] and has been referred to as the Uspensky algorithm, the Vincent–Akritas–Collins algorithm, or Descartes method, although Descartes, Vincent and Uspensky ...
General methods: Bisection method — simple and robust; linear convergence Lehmer–Schur algorithm — variant for complex functions; Fixed-point iteration; Newton's method — based on linear approximation around the current iterate; quadratic convergence Kantorovich theorem — gives a region around solution such that Newton's method converges
In numerical analysis, inverse quadratic interpolation is a root-finding algorithm, meaning that it is an algorithm for solving equations of the form f(x) = 0. The idea is to use quadratic interpolation to approximate the inverse of f. This algorithm is rarely used on its own, but it is important because it forms part of the popular Brent's method.