Difference between revisions of "Lagrange interpolation (dup)"

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Constructs a polynomial of degree n through n+1 given points.
+
Constructs a polynomial of degree <math>n</math> through <math>n+1</math> given points.
 
Points can be added by clicking on "Add point".
 
Points can be added by clicking on "Add point".
 
<html>
 
<html>
 
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
 
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/prototype.js"></script>
 
 
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
 
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
 
<form><input type="button" value="Add point" onClick="addPoint()"></form>
 
<form><input type="button" value="Add point" onClick="addPoint()"></form>
 
<div id="box" class="jxgbox" style="width:600px; height:400px;"></div>
 
<div id="box" class="jxgbox" style="width:600px; height:400px;"></div>
 
<script language="JavaScript">
 
<script language="JavaScript">
        board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25});
+
var board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25, axis:true});
        // Axes
+
var p = [];
        b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
+
p[0] = board.create('point', [-1,2], {style:6});
        b1axisy = board.createElement('axis', [[0,0], [0,1]], {});
+
p[1] = board.create('point', [3,-1], {style:6});
 +
p[2] = board.create('point', [-3,0], {style:6});
 +
var graph = board.create('functiongraph', [board.lagrangePolynomial(p), -10, 10]);
  
        var p = [];
+
function addPoint() {
        p[0] = board.createElement('point', [-1,2], {style:6});
+
      p.push(board.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
        p[1] = board.createElement('point', [3,-1], {style:6});
+
      board.update();
        var polynomial = function(x) {
+
}
                var i;
 
                var y = 0.0;
 
                var xc = [];
 
                for (i=0;i<p.length;i++) {
 
                  xc[i] = p[i].X();
 
                }
 
                for (i=0;i<p.length;i++) {
 
                  var t = p[i].Y();
 
                  for (var k=0;k<p.length;k++) {
 
                    if (k!=i) {
 
                      t *= (x-xc[k])/(xc[i]-xc[k]);
 
                    }
 
                  }
 
                  y += t;
 
                }
 
                return y;
 
            };
 
        graph = board.createElement('curve', ['x', polynomial, 'x', -10, 10], {curveType:'graph'});
 
 
 
        function addPoint() {
 
          p.push(board.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
 
          board.update();
 
        }
 
         
 
 
</script>
 
</script>
 
</html>
 
</html>
Line 46: Line 23:
 
* [http://en.wikipedia.org/wiki/Lagrange_polynomial http://en.wikipedia.org/wiki/Lagrange_polynomial]
 
* [http://en.wikipedia.org/wiki/Lagrange_polynomial http://en.wikipedia.org/wiki/Lagrange_polynomial]
  
=== The underlying JavaaScript code ===
+
=== The underlying JavaScript code ===
 +
<source lang="html4strict">
 +
<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
 +
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
 +
<div id="box" class="jxgbox" style="width:600px; height:400px;"></div>
 +
</source>
 +
 
 
<source lang="javascript">
 
<source lang="javascript">
        board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25});
+
var board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25, axis:true});
        // Axes
+
var p = [];
        b1axisx = board.createElement('axis', [[0,0], [1,0]], {});
+
p[0] = board.create('point', [-1,2], {style:6});
        b1axisy = board.createElement('axis', [[0,0], [0,1]], {});
+
p[1] = board.create('point', [3,-1], {style:6});
 
+
p[2] = board.create('point', [-3,0], {style:6});
        var p = [];
+
var graph = board.create('functiongraph', [board.lagrangePolynomial(p), -10, 10]);
        p[0] = board.createElement('point', [-1,2], {style:6});
 
        p[1] = board.createElement('point', [3,-1], {style:6});
 
       
 
        var polynomial = function(x) {
 
                var i;
 
                var y = 0.0;
 
                var xc = [];
 
                for (i=0;i<p.length;i++) {
 
                  xc[i] = p[i].X();
 
                }
 
                for (i=0;i<p.length;i++) {
 
                  var t = p[i].Y();
 
                  for (var k=0;k<p.length;k++) {
 
                    if (k!=i) {
 
                      t *= (x-xc[k])/(xc[i]-xc[k]);
 
                    }
 
                  }
 
                  y += t;
 
                }
 
                return y;
 
            };
 
        graph = board.createElement('curve', ['x', polynomial, 'x', -10, 10], {curveType:'graph'});
 
 
 
        function addPoint() {
 
          p.push(board.createElement('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
 
          board.update();
 
        }
 
  
 +
function addPoint() {
 +
      p.push(board.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
 +
      board.update();
 +
}
 
</source>
 
</source>
  
  
[[Category:Examples]]
+
[[Category:Austragungsstueberl]]
 +
Category:Examples
 +
Category:Calculus
 +
Category:Interpolation

Latest revision as of 10:05, 8 June 2011

Constructs a polynomial of degree [math]n[/math] through [math]n+1[/math] given points. Points can be added by clicking on "Add point".

References

The underlying JavaScript code

<link rel="stylesheet" type="text/css" href="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraph.css" />
<script type="text/javascript" src="http://jsxgraph.uni-bayreuth.de/distrib/jsxgraphcore.js"></script>
<div id="box" class="jxgbox" style="width:600px; height:400px;"></div>
var board = JXG.JSXGraph.initBoard('box', {originX: 250, originY: 250, unitX: 50, unitY: 25, axis:true});
var p = [];
p[0] = board.create('point', [-1,2], {style:6});
p[1] = board.create('point', [3,-1], {style:6});
p[2] = board.create('point', [-3,0], {style:6});
var graph = board.create('functiongraph', [board.lagrangePolynomial(p), -10, 10]);

function addPoint() {
      p.push(board.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{style:6}));
      board.update();
}

Category:Examples Category:Calculus Category:Interpolation