Newton’s method

E803455

numerical method optimization method root-finding algorithm

Newton’s method is an iterative numerical technique used to find successively better approximations to the roots of a real-valued function.

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Observed surface forms (1)

Surface form	Occurrences
Newton method	1

Statements (47)

Predicate	Object
instanceOf	numerical method ⓘ optimization method ⓘ root-finding algorithm ⓘ
advantage	fast local convergence ⓘ high accuracy near root ⓘ
alsoKnownAs	Newton–Raphson method NERFINISHED ⓘ
appliesTo	differentiable functions ⓘ
assumes	nonzero derivative near root ⓘ
category	open root-finding method ⓘ
convergenceDependsOn	quality of initial guess ⓘ smoothness of the function ⓘ
convergenceType	quadratic convergence near a simple root ⓘ
disadvantage	can converge to an unintended root ⓘ can oscillate between points ⓘ may diverge for poor initial guesses ⓘ requires derivative information ⓘ
generalizedTo	multivariate functions ⓘ systems of nonlinear equations ⓘ
geometricInterpretation	intersection of tangent line with x-axis ⓘ
historicalOrigin	developed by Isaac Newton in the 17th century ⓘ independently developed by Joseph Raphson ⓘ
implementedIn	scientific computing libraries ⓘ
mayFailIf	derivative at iterate is very small ⓘ derivative at iterate is zero ⓘ function is not differentiable at iterate ⓘ initial guess is far from any root ⓘ
multivariateUpdateFormula	x_{n+1} = x_n - J_f(x_n)^{-1} f(x_n) ⓘ
namedAfter	Isaac Newton NERFINISHED ⓘ Joseph Raphson NERFINISHED ⓘ
relatedTo	fixed-point iteration ⓘ gradient-based optimization ⓘ secant method ⓘ
requires	derivative evaluation ⓘ function evaluation ⓘ
requiresInitialValue	initial guess x_0 ⓘ
stoppingCriterion	small change between successive iterates ⓘ small function value at iterate ⓘ
updateFormula	x_{n+1} = x_n - f(x_n)/f'(x_n) ⓘ
usedFor	finding roots of real-valued functions ⓘ finding zeros of differentiable functions ⓘ solving nonlinear equations ⓘ
usedIn	computer graphics ⓘ engineering computations ⓘ machine learning optimization ⓘ numerical analysis ⓘ scientific computing ⓘ
uses	Jacobian matrix for systems ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Halley’s method for solving equations → generalizationOf → Newton’s method ⓘ

Nonlinear programming → hasMethod → Newton’s method ⓘ

this entity surface form: Newton method