hw3

hw3

by yi hom

JavaScript

var num = [1,-35.3,495.5,-3470.5,12271.5,-18502.2,4536];

function f(x,a) {
	return ((((((((((((a[0])*x)+a[1])*x)+a[2])*x)+a[3])*x)+a[4])*x)+a[5])*x)+a[6];
}


var eval0 = function (x,a, derivatives) {
    var deriv = derivatives || 0;   // default argument
    //var fx = x*x*x - 3*x*x - x + 9;
    // Horner method
    var fx = ((((((((((((a[0])*x)+a[1])*x)+a[2])*x)+a[3])*x)+a[4])*x)+a[5])*x)+a[6];
    
    if (deriv === 0) 
        return [fx];
    else {
    	//var dfx = 3*x*x - 6*x - 1;
        var dfx = ((((((((((a[0]*6)*x)+a[1]*5)*x)+a[2]*4)*x)+a[3]*3)*x)+a[4]*2)*x)+a[5];
    	return [fx,dfx];
    }
}


function bisection (func, xLo, xHi, eps) {
    if (func(xLo,num) * func (xHi,num) > 0)
        return undefined;
    
	var xMid, fHi, fLo, fMid;
	fHi = func(xHi,num);   // fb
	fLo = func(xLo,num);   // fa
	var iter = 0;
    while (xHi - xLo > eps) {
        ++iter;
		xMid = (xLo+xHi)/2;
		fMid = func(xMid,num);  // 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];
}



function Newton (eval, x0, epsilon) {
    var eps = epsilon || 1e-4;
 	var imax = 20;
    for (var i = 0; i < imax; i++) {
        var fdf = eval (x0,num, 1);
        x1 = x0 - fdf[0]/fdf[1];
        console.log(x0);
        if (Math.abs(x1 - x0) < eps)
            break;
        x0 = x1;
    }
    return [x1, i];  // return [approx. root, iterations]
}


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


var result = Newton (eval0,1 , 1e-4);
alert ('Newton '+'in ' + result[1] + ' iterations: ' +
            'f(' + result[0] + ') = ' + eval0 (result[0],num,0) );