Newton's Method (newtons_method)

Newton's method for finding the root of a differentiable, univariate, scalar-valued function.

newtons_method

Newton's method for finding the root of a differentiable, univariate, scalar-valued function.

Syntax

x = newtons_method(f,df,x0)
x = newtons_method(f,df,x0,opts)
[x,k] = newtons_method(__)
[x,k,x_all] = newtons_method(__)

Description

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 to true (defaults to false)
• 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.

Examples and Additional Documentation

• 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.