fsolve

Syntax

x = fsolve(@func,x0)

x = fsolve(@func,x0,options)

[x,fval,info,output] = fsolve(...)

Inputs

func

The system to solve. See the optimset option Jacobian for details.

x0

An estimate of the solution.

options

A struct containing option settings.

See optimset for details.

Outputs

x

A solution of the system.

fval

The value of func evaulated at x.

info

The convergence status flag.

info = 4

Relative step size converged to within tolX.

info = 3

Relative function value converged to within tolFun.

info = 2

Step size converged to within tolX.

info = 1

Function value converged to within tolFun.

info = 0

Reached maximum number of iterations or function calls, or the algorithm aborted because it was not converging.

info = -3

Trust region became too small to continue.

output

A struct containing iteration details. The members are as follows:

iterations

The number of iterations.

nfev

The number of function evaluations.

xiter

The candidate solution at each iteration.

fvaliter

The objective function value at each iteration.

Examples

function res = SysFunc(x)
    % intersection of two paraboloids and a plane
    v1 = (x(1))^2 + (x(2))^2 + 6;
    v2 = 2*(x(1))^2 + 2*(x(2))^2 + 4;
    v3 = 5*x(1) - 5*x(2);
    res = zeros(2,1);
    res(1,1) = v1 - v3;
    res(2,1) = v2 - v3;
end

x0 = [1; 2];
[x,fval] = fsolve(@SysFunc,x0)

x = [Matrix] 2 x 1
 1.40000
-0.20000
fval = [Matrix] 2 x 1
3.67339e-07
7.34677e-07

function res = SysFunc(x, offset)
    % intersection of two paraboloids and a plane
    v1 = (x(1))^2 + (x(2))^2 + offset(1);
    v2 = 2*(x(1))^2 + 2*(x(2))^2 + offset(2);
    v3 = 5*x(1) - 5*x(2) + offset(3);
    res = zeros(2,1);
    res(1,1) = v1 - v3;
    res(2,1) = v2 - v3;
end

handle = @(x) SysFunc(x, [8,6,4]);
[x,fval] = fsolve(handle,x0)

x = [Matrix] 2 x 1
1.40000
0.20000
fval = [Matrix] 2 x 1
0
0

Comments

fsolve uses a modified Gauss-Netwon algorithm with a trust region method.

Options for convergence tolerance controls and analytical derivatives are specified with optimset.

If fsolve converges to a solution that is not a zero of the system, it will produce a warning indicating that a best fit value is being returned.

To pass additional parameters to a function argument, use an anonymous function.