fzero — Find scalar function zeros with bracketed root-finding in MATLAB and RunMat.

x = fzero(fun, x0) searches near a binary32 or binary64 scalar initial point x0 for a sign-changing bracket, then refines the root with a Brent-style method. x = fzero(fun, [a b]) uses the supplied bracket directly. Optional outputs follow MATLAB's standard contract: [x, fval], [x, fval, exitflag], and [x, fval, exitflag, output].

Syntax

x = fzero(fun, x0)
x = fzero(fun, x0, options)
[x, fval] = fzero(fun, x0)
[x, fval] = fzero(fun, x0, options)
[x, fval, exitflag] = fzero(fun, x0)
[x, fval, exitflag] = fzero(fun, x0, options)
[x, fval, exitflag, output] = fzero(fun, x0)
[x, fval, exitflag, output] = fzero(fun, x0, options)

Inputs

Returns

Returned values from fzero depend on how many outputs the caller requests.

Errors

How fzero works

• The function handle must return a finite real scalar. A binary32 initial point or interval is threaded through callback arguments and numeric outputs; when TolX is not explicit, either a binary32 initial point or interval or a binary32 initial function value selects eps('single') instead of eps('double').
• Strict compatibility mode rejects typed-integer or logical initial points, intervals, and function values. RunMat extension mode accepts those values when every integer converts exactly to binary64.
• Typed-integer option controls are a separately gated RunMat extension. Structural counts such as MaxIter and MaxFunEvals are validated as exact nonnegative integers rather than rounded through floating point.
• 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.
• fval is the function value at the returned x; exitflag is 1 for convergence and 0 when the iteration/function-evaluation budget is exhausted.
• The four-output output struct contains iterations, funcCount, algorithm, and message fields.
• Requests for more than four outputs are rejected.
• 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

Return the root and function value

f = @(x) x.^2 - 4;
[x, fval] = fzero(f, [0 3])

Expected output:

x =
    2.0000
fval =
     0

Set a tighter tolerance

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

Expected output:

x =
    3.1416

Using fzero with coding agents

Open a RunMat example with live inputs, then ask the agent to explain how fzero changes the result.

Related Math functions

Open-source implementation

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

• View the source for fzero in Rust on GitHub
• Learn how the RunMat runtime works
• Found a bug? Open an issue with a minimal reproduction.

About RunMat

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