Multivariate Newton's method
GPTKB entity
Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
Numerical algorithm
|
| gptkbp:alsoKnownAs |
gptkb:Newton–Raphson_method_for_systems
|
| gptkbp:application |
gptkb:Physics
Economics Engineering Optimization |
| gptkbp:appliesTo |
Systems of nonlinear equations
|
| gptkbp:convergenceType |
Quadratic (under certain conditions)
|
| gptkbp:convergesTo |
Root of system
|
| gptkbp:field |
gptkb:Mathematics
Numerical analysis |
| gptkbp:generalizes |
gptkb:Newton's_method_(univariate)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Multivariate Newton's method
|
| 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 |
| gptkbp:namedAfter |
gptkb:Joseph_Raphson
gptkb:Isaac_Newton |
| gptkbp:produces |
Sequence of approximations
|
| gptkbp:requires |
Jacobian to be invertible
|
| gptkbp:uses |
Jacobian matrix
Function vector Initial guess |
| gptkbp:bfsParent |
gptkb:Newton–Raphson_method
|
| gptkbp:bfsLayer |
6
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