x = fsolve(fun, x0)
[x, fval, exitflag, output, jacobian] = fsolve(fun, x0, options)
x = fsolve(problem)
| Parameter | Description |
|---|---|
| fun | function returning equation residuals. |
| x0 | initial point. |
| options | solver options. |
| Parameter | Description |
|---|---|
| x | estimated root, with the shape of x0. |
| fval | residual at x, with the shape returned by fun. |
| exitflag | reason the solver stopped: 1 (function values near zero), 2 (step below StepTolerance), 3 (residual change below FunctionTolerance), 4 (search direction below StepTolerance), 0 (iteration or evaluation limit), -1 (stopped by output function), -2 (converged to a point that is not a root), -3 (trust region or regularization collapse). |
| output | structure with iterations, funcCount, algorithm, firstorderopt and message fields. |
| jacobian | final Jacobian approximation. |
fsolve solves systems of nonlinear equations F(x) = 0.
The Algorithm option selects the engine: 'trust-region-dogleg' (default, square systems), 'trust-region' or 'levenberg-marquardt'. Non-square systems automatically switch to Levenberg-Marquardt with a warning.
The default MaxFunctionEvaluations is 100*numberOfVariables, MaxIterations is 400 and FunctionTolerance and StepTolerance are 1e-6. The Display option supports 'off', 'none', 'final', 'final-detailed', 'notify', 'notify-detailed', 'iter' and 'iter-detailed'.
If Jacobian is 'on' or SpecifyObjectiveGradient is true, fun must also return the Jacobian of the residuals.
fun = @(x) [x(1) - 3; x(2) + 4];
[x, fval] = fsolve(fun, [0; 0])| Version | Description |
|---|---|
| 2.0.0 | initial version |