Newton's root finding method - Revision history

A WASSERMANN at 13:54, 15 January 2021

2021-01-15T13:54:58Z

← Older revision		Revision as of 13:54, 15 January 2021
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	brd.on('update', xval);		brd.on('update', xval);
			// Initial call of xval()
	xval();		xval();

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	}		}

	brd.~~addHook~~(xval);		brd.on('update', xval);
			// Initial call of xval()
			xval();

	function newton(p, i, board) {		function newton(p, i, board) {

A WASSERMANN at 13:53, 15 January 2021

2021-01-15T13:53:43Z

← Older revision		Revision as of 13:53, 15 January 2021
Line 55:		Line 55:

	brd.on('update', xval);		brd.on('update', xval);
			xval();

	function newton(p, i, board) {		function newton(p, i, board) {

A WASSERMANN at 13:53, 15 January 2021

2021-01-15T13:53:20Z

← Older revision		Revision as of 13:53, 15 January 2021
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	}		}

	brd.~~addHook~~(xval);		brd.on('update', xval);

	function newton(p, i, board) {		function newton(p, i, board) {

A WASSERMANN at 13:51, 15 January 2021

2021-01-15T13:51:57Z

← Older revision		Revision as of 13:51, 15 January 2021
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	function newton(p, i, board) {		function newton(p, i, board) {
	board.suspendUpdate();		board.suspendUpdate();
	if(i > 0) {		if (i > 0) {
	var f = board.create('glider', [function(){ return p.X(); }, function(){ return g.Y(p.X()) }, g], {		var f = board.create('glider', [function(){ return p.X(); }, function(){ return g.Y(p.X()) }, g], {
	name: '', style: 3, color: 'green'});		name: '', style: 3, color: 'green'});
	//var l = board.create('segment', [p, f], {strokeWidth: 0.5, dash: 1, strokeColor: 'black'});		var l = board.create('segment', [p, f], {strokeWidth: 0.5, dash: 1, strokeColor: 'black'});
	var t = board.create('tangent', [f], {strokeWidth: 0.5, strokeColor: '#0080c0', dash: 0});		var t = board.create('tangent', [f], {strokeWidth: 0.5, strokeColor: '#0080c0', dash: 0});
	var x = board.create('intersection', [ax, t, 0],{name: 'x_{' + (steps - i + 1) + '}', style: 4, color: 'red'});		var x = board.create('intersection', [ax, t, 0],{name: 'x_{' + (steps - i + 1) + '}', style: 4, color: 'red'});
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	var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-5, 5, 5, -5], axis:true});		var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-5, 5, 5, -5], axis:true});
	var ax = brd.defaultAxes.x;		var ax = brd.defaultAxes.x;
	~~var ay = brd.defaultAxes.y;~~

	var g = brd.create('functiongraph', [term], {strokeWidth: 2});		var g = brd.create('functiongraph', [term], {strokeWidth: 2});
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	function newton(p, i, board) {		function newton(p, i, board) {
	board.suspendUpdate();		board.suspendUpdate();
	if(i > 0) {		if (i > 0) {
	var f = board.create('glider', [function(){ return p.X(); }, function(){ return g.Y(p.X()) }, g], {		var f = board.create('glider', [function(){ return p.X(); }, function(){ return g.Y(p.X()) }, g], {
	name: '', style: 3, color: 'green'});		name: '', style: 3, color: 'green'});
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	function newGraph(v) {		function newGraph(v) {
	g.generateTerm('x', 'x', v);		g.generateTerm('x', 'x', v);
			//g.updateCurve();
	brd.update();		brd.update();
	}		}

A WASSERMANN at 13:42, 15 January 2021

2021-01-15T13:42:15Z

← Older revision		Revision as of 13:42, 15 January 2021
Line 61:		Line 61:
	var f = board.create('glider', [function(){ return p.X(); }, function(){ return g.Y(p.X()) }, g], {		var f = board.create('glider', [function(){ return p.X(); }, function(){ return g.Y(p.X()) }, g], {
	name: '', style: 3, color: 'green'});		name: '', style: 3, color: 'green'});
	var l = board.create('segment', [p, f], {strokeWidth: 0.5, dash: 1, strokeColor: 'black'});		//var l = board.create('segment', [p, f], {strokeWidth: 0.5, dash: 1, strokeColor: 'black'});
	var t = board.create('tangent', [f], {strokeWidth: 0.5, strokeColor: '#0080c0', dash: 0});		var t = board.create('tangent', [f], {strokeWidth: 0.5, strokeColor: '#0080c0', dash: 0});
	var x = board.create('intersection', [ax, t, 0],{name: 'x_{' + (steps - i + 1) + '}', style: 4, color: 'red'});		var x = board.create('intersection', [ax, t, 0],{name: 'x_{' + (steps - i + 1) + '}', style: 4, color: 'red'});

A WASSERMANN at 13:41, 15 January 2021

2021-01-15T13:41:35Z

← Older revision		Revision as of 13:41, 15 January 2021
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	function newGraph(v) {		function newGraph(v) {
	g.generateTerm('x', 'x', v);		g.generateTerm('x', 'x', v);
	g.updateCurve();		//g.updateCurve();
	brd.update();		brd.update();
	}		}

A WASSERMANN at 13:40, 15 January 2021

2021-01-15T13:40:41Z

← Older revision		Revision as of 13:40, 15 January 2021
Line 41:		Line 41:
	var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-5, 5, 5, -5], axis:true});		var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-5, 5, 5, -5], axis:true});
	var ax = brd.defaultAxes.x;		var ax = brd.defaultAxes.x;
	~~var ay = brd.defaultAxes.y;~~

	var g = brd.create('functiongraph', [term], {strokeWidth: 2});		var g = brd.create('functiongraph', [term], {strokeWidth: 2});
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	===The underlying JavaScript code===		===The underlying JavaScript code===

	<source lang="xml">		<source lang="xml">
	<table width="600" border="0" cellpadding="0" cellspacing="0">		<table width="600" border="0" cellpadding="0" cellspacing="0">

A WASSERMANN at 13:31, 15 January 2021

2021-01-15T13:31:03Z

← Older revision		Revision as of 13:31, 15 January 2021
Line 72:		Line 72:
	function newGraph(v) {		function newGraph(v) {
	g.generateTerm('x', 'x', v);		g.generateTerm('x', 'x', v);
			g.updateCurve();
	brd.update();		brd.update();
	}		}

A WASSERMANN at 13:26, 15 January 2021

2021-01-15T13:26:59Z

← Older revision		Revision as of 13:26, 15 January 2021
Line 92:		Line 92:
	<tr><td> </td></tr>		<tr><td> </td></tr>
	<script type="text/javascript">		<script type="text/javascript">
	// ~~Initial~~ function term		// Get initial function term
	var term = ~~function~~(x) ~~{ return xxx/5; };~~		var term = document.getElementById('graphterm').value;
	~~var graph = function(x) { return term(x); }~~;

	// Recursion depth		// Recursion depth
	var steps = 11;		var steps = 11;
	// Start value
	var s = 3;		// Start value for x
			var x_0 = 3;

	for (i = 0; i < steps; i++) {		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>');		document.write('<tr><td><nobr>x<sub>' + i + '</sub> = </nobr></td><td><font id="xv' + i + '"></font></td></tr>');
	}		}
	</script>		<</script>
	</table>		</table>
	</source>		</source>
Line 110:		Line 110:
	<source lang="javascript">		<source lang="javascript">
	var i;		var i;
	var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-5,5,5,-5], axis:~~false~~});		var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-5, 5, 5, -5], axis:true});
	var ax = brd.~~create('axis', [[0,0], [1,0]], {strokeColor: 'black'})~~;		var ax = brd.defaultAxes.x;
	var ay = brd.~~create('axis', [[0,0], [0,1]], {strokeColor: 'black'})~~;		var ay = brd.defaultAxes.y;

	var g = brd.create('functiongraph', [~~function(x){return graph(x);}~~],{strokeWidth: 2~~, dash:0~~});		var g = brd.create('functiongraph', [term], {strokeWidth: 2});
	var x = brd.create('glider',[s,0,ax], {name: 'x_{0}', ~~strokeColor~~: 'magenta', ~~fillColor~~: ~~'yellow'~~});		var x = brd.create('glider', [x_0, 0, ax], {name: 'x_{0}', color: 'magenta', size: 4});

	newGraph(document.getElementById('graphterm').value);		newGraph(document.getElementById('graphterm').value);
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	function xval() {		function xval() {
	for (i = 0; i < steps; i++)		for (i = 0; i < steps; i++) {
	document.getElementById('xv' + i).innerHTML = (brd.select('x_{' + i + '}').X()).toFixed(14);		document.getElementById('xv' + i).innerHTML = (brd.select('x_{' + i + '}').X()).toFixed(14);
			}
	}		}

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	function newton(p, i, board) {		function newton(p, i, board) {
	board.suspendUpdate();		board.suspendUpdate();
	if(i>0) {		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 f = board.create('glider', [function(){ return p.X(); }, function(){ return g.Y(p.X()) }, g], {
	var l = board.create('~~line~~', [p,f],{strokeWidth: 0.5, dash: 1~~, straightFirst: false, straightLast: false~~, strokeColor: 'black'});		name: '', style: 3, color: 'green'});
	var t = board.create('tangent',[f],{strokeWidth: 0.5, strokeColor: '#0080c0', dash: 0});		var l = board.create('segment', [p, f], {strokeWidth: 0.5, dash: 1, strokeColor: 'black'});
	var x = board.create('intersection',[ax,t,0],{name: 'x_{'+(steps-i+1) + '}', style: 4, ~~strokeColor: 'magenta', fillColor~~: '~~yellow~~'});		var t = board.create('tangent', [f], {strokeWidth: 0.5, strokeColor: '#0080c0', dash: 0});
	newton(x,--i, board);		var x = board.create('intersection', [ax, t, 0],{name: 'x_{' + (steps - i + 1) + '}', style: 4, color: 'red'});
			newton(x, --i, board);
	}		}
	board.unsuspendUpdate();		board.unsuspendUpdate();
	}		}

	function newGraph(v) {		function newGraph(v) {
	~~eval("term = function(x){ return "+v+";}");~~		g.generateTerm('x', 'x', v);
	~~graph = function(x) { return term(x); };~~		brd.update();
	g.~~Y = function~~(x~~){ return term(~~x~~); };~~
	~~g.updateCurve(~~);
	brd.update();
	}		}
	</source>		</source>

A WASSERMANN at 13:26, 15 January 2021

2021-01-15T13:26:07Z

← Older revision		Revision as of 13:26, 15 January 2021
Line 29:		Line 29:

	// Start value for x		// Start value for x
	var s = 3;		var x_0 = 3;

	for (i = 0; i < steps; i++) {		for (i = 0; i < steps; i++) {
Line 40:		Line 40:
	var i;		var i;
	var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-5, 5, 5, -5], axis:true});		var brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-5, 5, 5, -5], axis:true});
	~~//var ax = brd.create('axis', [[0,0], [1,0]], {strokeColor: 'black'});~~
	~~//var ay = brd.create('axis', [[0,0], [0,1]], {strokeColor: 'black'});~~
	var ax = brd.defaultAxes.x;		var ax = brd.defaultAxes.x;
	var ay = brd.defaultAxes.y;		var ay = brd.defaultAxes.y;

	var g = brd.create('functiongraph', [term],{strokeWidth: 2~~, dash:0~~});		var g = brd.create('functiongraph', [term], {strokeWidth: 2});
	var x = brd.create('glider', [s, 0, ax], {name: 'x_{0}', ~~strokeColor~~: 'magenta', ~~fillColor~~: ~~'yellow'~~});		var x = brd.create('glider', [x_0, 0, ax], {name: 'x_{0}', color: 'magenta', size: 4});

	newGraph(document.getElementById('graphterm').value);		newGraph(document.getElementById('graphterm').value);
Line 52:		Line 50:

	function xval() {		function xval() {
	for (i = 0; i < steps; i++)		for (i = 0; i < steps; i++) {
	document.getElementById('xv' + i).innerHTML = (brd.select('x_{' + i + '}').X()).toFixed(14);		document.getElementById('xv' + i).innerHTML = (brd.select('x_{' + i + '}').X()).toFixed(14);
			}
	}		}

Line 60:		Line 59:
	function newton(p, i, board) {		function newton(p, i, board) {
	board.suspendUpdate();		board.suspendUpdate();
	if(i>0) {		if(i > 0) {
	var f = board.create('glider',[function(){return p.X();}, function(){return g.Y(p.X())}, g], {name: '', style: 3, ~~strokeColor~~: 'green~~', fillColor: 'yellow~~'});		var f = board.create('glider', [function(){ return p.X(); }, function(){ return g.Y(p.X()) }, g], {
	var l = board.create('~~line~~', [p,f],{strokeWidth: 0.5, dash: 1~~, straightFirst: false, straightLast: false~~, strokeColor: 'black'});		name: '', style: 3, color: 'green'});
	var t = board.create('tangent',[f],{strokeWidth: 0.5, strokeColor: '#0080c0', dash: 0});		var l = board.create('segment', [p, f], {strokeWidth: 0.5, dash: 1, strokeColor: 'black'});
	var x = board.create('intersection',[ax,t,0],{name: 'x_{'+(steps-i+1) + '}', style: 4, ~~strokeColor: 'magenta', fillColor~~: '~~yellow~~'});		var t = board.create('tangent', [f], {strokeWidth: 0.5, strokeColor: '#0080c0', dash: 0});
	newton(x,--i, board);		var x = board.create('intersection', [ax, t, 0],{name: 'x_{' + (steps - i + 1) + '}', style: 4, color: 'red'});
			newton(x, --i, board);
	}		}
	board.unsuspendUpdate();		board.unsuspendUpdate();
	}		}

	function newGraph(v) {		function newGraph(v) {
	/*		g.generateTerm('x', 'x', v);
	~~eval("term = function(x){ return "+v+";}");~~		brd.update();
	~~graph = function(x) { return term(x); };~~
	~~g.Y = function(x){ return term(x); };~~
	~~g.updateCurve();~~
	*/
	g.generateTerm('x', 'x', v);
	brd.update();
	}		}
	</jsxgraph>		</jsxgraph>