Newton's method (univariate)

URI: https://gptkb.org/entity/Newton's_method_(univariate)
GPTKB entity
Statements (28)
Predicate Object
gptkbp:instanceOf Numerical method
gptkbp:alsoKnownAs gptkb:Newton–Raphson_method
gptkbp:application gptkb:Mathematics
gptkb:Physics
Engineering
Computer science
gptkbp:category Root-finding algorithms
Numerical analysis
gptkbp:convergenceType Quadratic convergence (near root)
gptkbp:failsWhen Derivative is zero at guess
Function is not differentiable
gptkbp:firstPublished gptkb:Raphson:_1690
Newton: 1671 (published 1736)
gptkbp:form x_{n+1} = x_n - f(x_n)/f'(x_n)
gptkbp:generalizes gptkb:Newton's_method_(multivariate)
https://www.w3.org/2000/01/rdf-schema#label Newton's method (univariate)
gptkbp:input Initial guess
Differentiable function
gptkbp:namedAfter gptkb:Joseph_Raphson
gptkb:Isaac_Newton
gptkbp:output Approximate root
gptkbp:relatedTo gptkb:Secant_method
Fixed-point iteration
gptkbp:requires Derivative of function
gptkbp:supportsAlgorithm Iterative method
gptkbp:usedFor Finding roots of real-valued functions
gptkbp:bfsParent gptkb:Multivariate_Newton's_method
gptkbp:bfsLayer 7