Newton–Raphson method for single variable

URI: https://gptkb.org/entity/Newton–Raphson_method_for_single_variable
GPTKB entity
Statements (30)
Predicate Object
gptkbp:instanceOf gptkb:Numerical_method
gptkbp:alsoKnownAs gptkb:Newton's_method
gptkbp:appliesTo Differentiable functions
gptkbp:canDiverge Yes, under certain conditions
gptkbp:category Root-finding algorithms
Numerical analysis
gptkbp:complexity Depends on function and initial guess
gptkbp:convergesTo Quadratically (under suitable conditions)
gptkbp:developedBy gptkb:Joseph_Raphson
gptkb:Isaac_Newton
gptkbp:failsWhen Derivative is zero at root
Initial guess is far from root
gptkbp:firstPublished 17th century
gptkbp:form x_{n+1} = x_n - f(x_n)/f'(x_n)
gptkbp:generalizes Newton–Raphson method for systems of equations
gptkbp:namedAfter gptkb:Joseph_Raphson
gptkb:Isaac_Newton
gptkbp:relatedTo gptkb:Secant_method
Fixed-point iteration
gptkbp:requires Derivative of the function
Initial guess
gptkbp:supportsAlgorithm Iterative method
gptkbp:usedFor Finding roots of real-valued functions
gptkbp:usedIn gptkb:Mathematics
gptkb:Physics
Engineering
Computer science
gptkbp:bfsParent gptkb:Newton–Raphson_method_for_systems
gptkbp:bfsLayer 8
https://www.w3.org/2000/01/rdf-schema#label Newton–Raphson method for single variable