Newton Raphson - Multiple functions

Newton-Raphson iterative method to find roots of a function (or multiple functions). Adjustable residue tolerance, max number of iterations

% Newton-Raphson iterative method to find roots of a function.

% Ex.: roots = NewtonRaphson(f, x, [tol], [MaxIt], [Delta])

%

% There are 2 mandatory inputs (f and x) and 3 optional arguments (tol,

% MaxIt, and Delta).

%

% The function returns 1 output (x).

%

% INPUTS:

% 1. f - function handle to which the roots should be found. It should

% be noted that if f is a multivariable function handle (for example, f =

% @(x, y) [x^2 + y^2 - 3^2; x - y = 3]), then the function handle

% should be rewritten as a one vector variable function handle (for

% example, f = @(x) [x(1)^2 + x(2)^2 - 3^2; x(1) - x(2) = 3]).

% Additionally, the output size of the function handle should always

% match the variable x size.

% 2. x - initial guess for the roots of the vector variable.

% 3. [Optional] tol - convergence tolerance.

% Type: Double. Default: 1e-3.

% 4. [Optional] MaxIt - Maximum number of iterations.

% Type: Double. Default: 1e3.

% 5. [Optional] Delta - Step for numerical derivative.

% Type: Double. Default: 1e-6.

%

% OUTPUTS:

% 1. roots - roots of the function. If the algorithm does not converge, then x

% is NaN. x is the same size and type as the input x.

%

% Examples:

% roots = NewtonRaphson(@(x) [x(1) - x(2) - 2; x(2) - 5], [0; 0])

% roots = NewtonRaphson(@(x) [x(1) - x(2) - 2; x(2) - 5], [0; 0]), 1e-6, 50, 1e-12)

%

% © Universidade de Brasilia, 2023

% Power Quality Laboratory (LQEE)

% Author: Victor do Prado Brasil

% Version History:

% 2023/07/13 - Creation of the function.