fsolve — Solve scalar or vector nonlinear equation systems using finite-difference Levenberg-Marquardt iterations.

x = fsolve(fun, x0) solves fun(x) = 0 starting from x0. Scalar guesses return scalars; vector and matrix guesses return a result with the same shape as x0.

How fsolve works

• The function handle must return a finite real scalar or vector.
• Jacobians are estimated with forward finite differences.
• The step is chosen with a Levenberg-Marquardt damping parameter and accepted only when it reduces the residual norm.
• Options are supplied as a struct, usually created with optimset. TolX, TolFun, MaxIter, MaxFunEvals, and Display are accepted.

Examples

Solve a two-variable nonlinear system

F = @(x) [x(1)^2 + x(2)^2 - 4; x(1)*x(2) - 1];
x = fsolve(F, [1; 1])

Expected output:

x =
    1.9319
    0.5176

Solve a scalar equation

x = fsolve(@sin, 3)

Expected output:

x =
    3.1416

Related Math functions

Open-source implementation

Unlike proprietary runtimes, every RunMat function is open-source. Read exactly how fsolve works, line by line, in Rust.

• View fsolve.rs on GitHub
• Learn how the runtime works
• Found a bug? Open an issue with a minimal reproduction.

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