Newton's method for finding the root of a differentiable, univariate, scalar-valued function.
x = newtons_method(f,df,x0)
x = newtons_method(f,df,x0,opts)
[x,k] = newtons_method(__)
[x,k,x_all] = newtons_method(__)
x = newtons_method(f,df,x0) returns the root of a function specified by the function handle
f, where df is the derivative of (i.e.
) and
x0 is an initial guess of the root.
x = newtons_method(f,df,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(__) also returns the number of iterations (k) performed of Newton's method.
[x,k,x_all] = newtons_method(__) 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.
- 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.