Fixed-point iteration for finding the fixed point of a univariate, scalar-valued function.

c = fixed_point_iteration(f,x0)
c = fixed_point_iteration(f,x0,opts)
[c,k] = fixed_point_iteration(__)
[c,k,c_all] = fixed_point_iteration(__)

c = fixed_point_iteration(f,x0) returns the fixed point of a function specified by the function handle f, where x0 is an initial guess of the fixed point.

c = fixed_point_iteration(f,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 )

[c,k] = fixed_point_iteration(__) also returns the number of iterations (k) performed of fixed-point iteration.

[c,k,c_all] = fixed_point_iteration(__) does the same as the previous syntaxes, but also returns an array (c_all) storing the fixed point 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.