Difference between revisions of "Newton's root finding method"

From JSXGraph Wiki
Jump to: navigation, search
Line 1: Line 1:
 
<html>
 
<html>
<table width="300" border="0" cellpadding="0" cellspacing="0">
+
<table width="600" border="0" cellpadding="0" cellspacing="0">
 
x<sub>o</sub> is the start value. Drag it.
 
x<sub>o</sub> is the start value. Drag it.
 
<p></p>
 
<p></p>
Line 8: Line 8:
 
<td>
 
<td>
 
<form>
 
<form>
<input style="border:none; background-color:#efefef;padding:5px;margin-left:2px;" type="text" id="graphterm" value="x*x*x/5" size="30"/><input type="button" value="set function term" onClick="newGraph(document.getElementById('graphterm').value);">
+
<input style="border:none; background-color:#efefef;padding:5px;margin-left:2px;" type="text" id="graphterm" value="x*x*x/5" size="30"/><input type="button" value="set term" onClick="newGraph(document.getElementById('graphterm').value);">
 
</form>
 
</form>
 
</td>
 
</td>
Line 70: Line 70:
  
 
===The underlying JavaScript code===
 
===The underlying JavaScript code===
 +
<source lang="xml">
 +
<table width="600" border="0" cellpadding="0" cellspacing="0">
 +
x<sub>o</sub> is the start value. Drag it.
 +
<p></p>
 +
You may change the function term here:
 +
<br>
 +
<td><nobr>f(x) = </nobr></td>
 +
<td>
 +
<form>
 +
<input style="border:none; background-color:#efefef;padding:5px;margin-left:2px;" type="text" id="graphterm" value="x*x*x/5" size="30"/><input type="button" value="set term" onClick="newGraph(document.getElementById('graphterm').value);">
 +
</form>
 +
</td>
 +
<tr><td>&nbsp;</td></tr>
 +
<script type="text/javascript">
 +
// Initial function term
 +
var term = function(x) { return x*x*x/5; };
 +
var graph = function(x) { return term(x); };
 +
 +
// Recursion depth
 +
var steps = 11;
 +
// Start value
 +
var s = 3;
 +
 +
for (i = 0; i < steps; i++) {
 +
    document.write('<tr><td><nobr>x<sub>' + i + '</sub> = </nobr></td><td><font id="xv' + i + '"></font></td></tr>');
 +
}
 +
</script>
 +
</table>
 +
<jsxgraph width="600" height="500">
 +
</source>
 +
<source lang="javascript">
 +
var i;
 +
var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-5,10,5,-2], axis:true});
 +
var ax = board.create('axis', [[0,0], [1,0]], {strokeColor: 'black'});
 +
var ay = board.create('axis', [[0,0], [0,1]], {strokeColor: 'black'});
 +
 +
var g = board.create('functiongraph', [function(x){return graph(x);}],{strokeWidth: 2, dash:0});
 +
var x = board.create('glider',[s,0,ax], {name: 'x_{0}', strokeColor: 'magenta', fillColor: 'yellow'});
 +
 +
newGraph(document.getElementById('graphterm').value);
 +
newton(x,steps);
 +
function xval(board) {
 +
    for (i = 0; i < steps; i++)
 +
        document.getElementById('xv' + i).innerHTML = board.round(JXG.getReference(board, 'x_{' + i + '}').X(),14);
 +
}
 +
 +
board.addHook(xval);
 +
 +
function newton(p, i) {
 +
    if(i>0) {
 +
        var f = board.create('glider',[function(){return p.X();}, function(){return graph(p.X())},g], {name: '', style: 3, strokeColor: 'green', fillColor: 'yellow'});
 +
        var l = board.create('line', [p,f],{strokeWidth: 0.5, dash: 1, straightFirst: false, straightLast: false, strokeColor: 'black'});
 +
        var t = board.create('tangent',[f],{strokeWidth: 0.5, strokeColor: '#0080c0', dash: 0});
 +
        var x = board.create('point',[board.intersection(ax,t,0)],{name: 'x_{'+(steps-i+1) + '}', style: 4, strokeColor: 'magenta', fillColor: 'yellow'});
 +
        newton(x,--i);
 +
    }
 +
}
 +
function newGraph(v) {
 +
eval("term = function(x){ return "+v+";}");
 +
graph = function(x) { return term(x); };
 +
g.Y = function(x){ return term(x); };
 +
g.updateCurve();
 +
        board.update();
 +
}
 +
</source>
 +
<source lang="xml">
 +
</jsxgraph>
 +
</source>
 +
 +
 +
[[Category:Examples]]
 +
[[Category:Calculus]]

Revision as of 15:22, 3 February 2010

xo is the start value. Drag it.

You may change the function term here:
f(x) =
 
You also may try the following function terms:

  • [math]Math.sin(x)[/math]
  • [math]Math.exp(x)[/math]
  • [math]Math.pow(2,x)[/math]
  • [math]1-2/(x*x)[/math]

The underlying JavaScript code

<table width="600" border="0" cellpadding="0" cellspacing="0">
x<sub>o</sub> is the start value. Drag it.
<p></p>
You may change the function term here:
<br>
<td><nobr>f(x) = </nobr></td>
<td>
<form>
<input style="border:none; background-color:#efefef;padding:5px;margin-left:2px;" type="text" id="graphterm" value="x*x*x/5" size="30"/><input type="button" value="set term" onClick="newGraph(document.getElementById('graphterm').value);">
</form>
</td>
<tr><td>&nbsp;</td></tr>
<script type="text/javascript">
// Initial function term
var term = function(x) { return x*x*x/5; };
var graph = function(x) { return term(x); };
	
// Recursion depth
var steps = 11;
// Start value
var s = 3;

for (i = 0; i < steps; i++) {
     document.write('<tr><td><nobr>x<sub>' + i + '</sub> = </nobr></td><td><font id="xv' + i + '"></font></td></tr>');
}
</script>		
</table> 
<jsxgraph width="600" height="500">
var i;
var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-5,10,5,-2], axis:true});
var ax = board.create('axis', [[0,0], [1,0]], {strokeColor: 'black'});
var ay = board.create('axis', [[0,0], [0,1]], {strokeColor: 'black'});

var g = board.create('functiongraph', [function(x){return graph(x);}],{strokeWidth: 2, dash:0});
var x = board.create('glider',[s,0,ax], {name: 'x_{0}', strokeColor: 'magenta', fillColor: 'yellow'});

newGraph(document.getElementById('graphterm').value);
newton(x,steps);	
function xval(board) {
    for (i = 0; i < steps; i++)
        document.getElementById('xv' + i).innerHTML = board.round(JXG.getReference(board, 'x_{' + i + '}').X(),14);
}

board.addHook(xval);

function newton(p, i) {		
    if(i>0) {
        var f = board.create('glider',[function(){return p.X();}, function(){return graph(p.X())},g], {name: '', style: 3, strokeColor: 'green', fillColor: 'yellow'});
        var l = board.create('line', [p,f],{strokeWidth: 0.5, dash: 1, straightFirst: false, straightLast: false, strokeColor: 'black'});
        var t = board.create('tangent',[f],{strokeWidth: 0.5, strokeColor: '#0080c0', dash: 0});
        var x = board.create('point',[board.intersection(ax,t,0)],{name: 'x_{'+(steps-i+1) + '}', style: 4, strokeColor: 'magenta', fillColor: 'yellow'});
        newton(x,--i);
    }
}	
function newGraph(v) {
	eval("term = function(x){ return "+v+";}");				
	graph = function(x) { return term(x); };
	g.Y = function(x){ return term(x); };
	g.updateCurve();
        board.update();
}
</jsxgraph>