Newton's method (multivariate)

URI: https://gptkb.org/entity/Newton's_method_(multivariate)
GPTKB entity
Statements (25)
Predicate Object
gptkbp:instanceOf gptkb:Numerical_algorithm
gptkbp:alsoKnownAs Multivariate Newton–Raphson method
gptkbp:application Nonlinear systems
Optimization (as Newton's method for optimization)
gptkbp:category Root-finding algorithms
Iterative methods
gptkbp:convergesTo Quadratic (under certain conditions)
gptkbp:field gptkb:Mathematics
Numerical analysis
gptkbp:firstDescribed 18th century
gptkbp:generalizes gptkb:Newton's_method_(univariate)
gptkbp:iterationFormula x_{n+1} = x_n - J_f(x_n)^{-1} f(x_n)
gptkbp:limitation May not converge if initial guess is poor
Requires computation of Jacobian inverse
gptkbp:namedAfter gptkb:Joseph_Raphson
gptkb:Isaac_Newton
gptkbp:relatedTo gptkb:Secant_method
gptkb:Broyden's_method
Quasi-Newton methods
gptkbp:requires Jacobian matrix
Initial guess
gptkbp:usedFor Finding roots of vector-valued functions
gptkbp:bfsParent gptkb:Newton's_method_(univariate)
gptkbp:bfsLayer 8
https://www.w3.org/2000/01/rdf-schema#label Newton's method (multivariate)