bisection

my example

by SunnyHsu

JavaScript

// function declaration 
function f(x) {
	return Math.sin (x) - 0.5*x;
}
/*
// function expression
var f = function (x) {
	return Math.sin (x) - 0.5*x;
};
*/

function ff(x) {
	return Math.cos(x) - 0.33*x;
}


function bisection (func, xLo, xHi, eps) {
    if (func(xLo) * func (xHi) > 0)
        return undefined;
    
	var xMid, fHi, fLo, fMid;
	fHi = func(xHi);   // fb
	fLo = func(xLo);   // fa
	var iter = 0;
    while (xHi - xLo > eps) {
        ++iter;
		xMid = (xLo+xHi)/2;
		fMid = func(xMid);  // fc
		//console.log ('f(c) = ' + fMid);
		if (Math.abs(fMid) < eps)
			return [xMid, iter];
		else if (fMid*fLo < 0) { // fa*fc < 0 --> [a,c]
			xHi = xMid;
			fHi = fMid;
		} else {  // fc*fb < 0 --> [c,b]
			xLo = xMid;
			fLo = fMid;
		}
	}
	return [(xLo+xHi)/2, iter];
}

var ans = bisection (ff, 1, 3, 1e-4);
alert ('in ' + ans[1] + ' iterations: ' + 'f(' + ans[0].toFixed(3) + ')= ' + ff(ans[0]).toExponential(3));
console.log('in ' + ans[1] + ' iterations: ' + 'f(' + ans[0].toFixed(3) + ')= ' + ff(ans[0]).toExponential(3));