Newton's method for finding the root of a differentiable, multivariate, vector-valued function.
x = newtons_method_n(f,J,x0)
x = newtons_method_n(f,J,x0,opts)
[x,k] = newtons_method_n(__)
[x,k,x_all] = newtons_method_n(__)
x = newtons_method_n(f,J,x0) returns the root of a multivariate, vector-valued function specified by the function handle
f, where J is the Jacobian of with respect to
(i.e.
) and where
x0 () is an initial guess of the root.
x = newtons_method_n(f,J,x0,opts) does the same as the syntax above, but allows for the specification of optional solver parameters. opts is a structure with the following fields:
k_max→ maximum number of iterations (defaults to 200)return_all→ returns estimates at all iteration if set totrue(defaults tofalse)TOL→ tolerance (defaults to)
[x,k] = newtons_method_n(__) also returns the number of iterations (k) performed of Newton's method.
[x,k,x_all] = newtons_method_n(__) does the same as the previous syntaxes, but also returns an array (x_all) storing the root estimates at each iteration. This syntax requires that opts.return_all be set to true.
- The Numerical Differentiation Toolbox provides functions for approximating the Jacobian.
- See "EXAMPLES.mlx" or the "Examples" tab on the File Exchange page for examples.
- See "Root_Finding_Methods.pdf" (also included with download) for the technical documentation.