Newton's method (multivariate)
GPTKB entity
Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
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)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Newton's method (multivariate)
|
| 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
|