fzero — Find a zero of a scalar nonlinear function using bracket expansion and Brent's method.

x = fzero(fun, x0) searches near the scalar initial point x0 for a sign-changing bracket, then refines the zero. x = fzero(fun, [a b]) uses the supplied two-element bracket directly.

How fzero works

• The function handle must return a finite real scalar.
• Bracket endpoints must have opposite signs unless one endpoint is already a root.
• Options are supplied as a struct, usually created with optimset. TolX, MaxIter, MaxFunEvals, and Display are accepted.
• Anonymous functions, named function handles, and function-handle strings work through RunMat's existing feval dispatch path.

Examples

Find the fixed point of cosine

f = @(x) cos(x) - x;
x = fzero(f, 0.5)

Expected output:

x =
    0.7391

Use an explicit bracket

x = fzero(@sin, [3 4])

Expected output:

x =
    3.1416

Set a tighter tolerance

opts = optimset('TolX', 1e-10, 'Display', 'off');
x = fzero(@sin, [3 4], opts)

Expected output:

x =
    3.1416

Related Math functions

Open-source implementation

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

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

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