README.md

brentq

Find a zero of a continuous function using Brent's method.

Finds a zero of a continuous function $f$ on the interval $\lbrack a, b \rbrack$ where the sign of $f(a)$ and $f(b)$ must be opposite.

Usage

var brentq = require( '@stdlib/optimize/base/brentq' );

brentq( f, a, b, maxIter, xtol, rtol, args )

Finds a zero of a continuous function f on the interval [a, b].

function f( x ) {
    return ( x * x ) - 1.0;
}

var out = brentq( f, 0.0, 2.0, 100, 2.0e-12, 8.88e-16, [] );
var root = out.root;
// returns 1.0

The function returns a solution object with the following properties:

• root: the root.
• iterations: number of iterations.
• function_calls: number of function calls.
• converged: boolean indicating if convergence was reached.
• flag: convergence condition message.
• method: method name.

The function has the following parameters:

• f: objective function f(x, ...args).
• a: lower bound.
• b: upper bound.
• maxIter: maximum number of iterations.
• xtol: absolute tolerance.
• rtol: relative tolerance.
• args: array of arguments to be passed to f.

Examples

var sin = require( '@stdlib/math/base/special/sin' );
var brentq = require( '@stdlib/optimize/base/brentq' );

function f( x ) {
    return sin( x );
}

var out = brentq( f, 3.0, 3.2, 100, 2e-12, 8.88e-16, [] );
var root = out.root;

console.log( root );
// => 3.141592653589793