This group gathers numerical algorithms that locate a root of a function or an optimum of an objective, including Newton-Raphson, the secant method, the bisection method, Brent's method, Muller's method, Bairstow's method, Broyden's method, and the Levenberg-Marquardt algorithm for nonlinear least squares. Their shared work is iteratively narrowing in on a single value, root or optimum that satisfies an equation or minimizes an error, as distinct from solving an entire linear system at once, which belongs to Linear Algebra and Matrix Decomposition, or integrating a function over a range, which belongs to Numerical Integration and Differential Equations.
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Root-Finding and Optimization
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1. Wikipedia: Newton's method
Wikimedia FoundationNewton's method, History section, De analysi sentenceQuote, Newton's method, History section, De analysi sentence
The method that laid the groundwork for what is now the modern Newton's method which would be developed by Joseph Raphson and Thomas Simpson first appeared in Isaac Newton's work in De analysi per aequationes numero terminorum infinitas (written in 1669, published in 1711 by William Jones) and in De metodis fluxionum et serierum infinitarum (written in 1671, translated and published as Method of Fluxions in 1736 by John Colson).
Square root algorithms (Wikipedia)
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Square root algorithms compute the non-negative square root
Steffensen's method (Wikipedia)
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an iterative method named after Johan Frederik Steffensen for numerical root-finding
Householder's method (Wikipedia)
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These methods are named after the American mathematician Alston Scott Householder.
Durand-Kerner method (Wikipedia)
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is a root-finding algorithm for solving polynomial equations
Laguerre's method (Wikipedia)
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Laguerre's method is a root-finding algorithm tailored to polynomials
Graeffe's method (Wikipedia)
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Graeffe's method or Dandelin-Lobachesky-Graeffe method is an algorithm for finding all of the roots of a polynomial.
Aitken's delta-squared process (Wikipedia)
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Aitken's delta-squared process or Aitken extrapolation is a series acceleration method used for accelerating the rate of convergence of a sequence.
Aberth method (Wikipedia)
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is a root-finding algorithm developed in 1967 for simultaneous approximation of all the roots of a univariate polynomial.
Gauss-Newton algorithm (Wikipedia)
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It is an extension of Newton's method for finding a minimum of a non-linear function.
Golden-section search (Wikipedia)
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The golden-section search is a technique for finding an extremum (minimum or maximum) of a function inside a specified interval.
Ridders' method (Wikipedia)
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Ridders' method is a root-finding algorithm based on the false position method
Jenkins-Traub algorithm (Wikipedia)
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a fast globally convergent iterative polynomial root-finding method
Inverse quadratic interpolation (Wikipedia)
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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.
Adjoint state method (Wikipedia)
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efficiently computing the gradient of a function or operator in a numerical optimization problem
ITP method (Wikipedia)
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the ITP method (Interpolate Truncate and Project method) is the first root-finding algorithm that achieves the superlinear convergence of the secant method while retaining the optimal worst-case performance of the bisection method.
Regula falsi (Wikipedia)
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a family of algorithms used to solve linear equations and smooth nonlinear equations for a single unknown value
Halley's method (Wikipedia)
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is a root-finding algorithm
Fixed-point iteration (Wikipedia)
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In numerical analysis, fixed-point iteration is a method of computing fixed points of a function.
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