Difference between revisions of "Lagrange interpolation"

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(One intermediate revision by the same user not shown)
Line 11: Line 11:
 
p[0] = board.create('point', [-1,2], {size:4});
 
p[0] = board.create('point', [-1,2], {size:4});
 
p[1] = board.create('point', [3,-1], {size:4});
 
p[1] = board.create('point', [3,-1], {size:4});
var f = board.lagrangePolynomial(p);
+
var f = JXG.Math.Numerics.lagrangePolynomial(p);
 
var graph = board.create('functiongraph', [f,-10, 10], {strokeWidth:3});
 
var graph = board.create('functiongraph', [f,-10, 10], {strokeWidth:3});
var d1 = board.create('functiongraph', [board.D(f), -10, 10], {dash:1});
+
var d1 = board.create('functiongraph', [JXG.Math.Numerics.D(f), -10, 10], {dash:1});
var d2 = board.create('functiongraph', [board.D(board.D(f)), -10, 10], {dash:2});
+
var d2 = board.create('functiongraph', [JXG.Math.Numerics.D(JXG.Math.Numerics.D(f)), -10, 10], {dash:2});
  
 
function addPoint() {
 
function addPoint() {
Line 32: Line 32:
 
p[0] = board.create('point', [-1,2], {size:4});
 
p[0] = board.create('point', [-1,2], {size:4});
 
p[1] = board.create('point', [3,-1], {size:4});
 
p[1] = board.create('point', [3,-1], {size:4});
var f = board.lagrangePolynomial(p);
+
var f = JXG.Math.Numerics.lagrangePolynomial(p);
 
var graph = board.create('functiongraph', [f,-10, 10], {strokeWidth:3});
 
var graph = board.create('functiongraph', [f,-10, 10], {strokeWidth:3});
var d1 = board.create('functiongraph', [board.D(f), -10, 10], {dash:1});
+
var d1 = board.create('functiongraph', [JXG.Math.Numerics.D(f), -10, 10], {dash:1});
var d2 = board.create('functiongraph', [board.D(board.D(f)), -10, 10], {dash:2});
+
var d2 = board.create('functiongraph', [JXG.Math.Numerics.D(JXG.Math.Numerics.D(f)), -10, 10], {dash:2});
  
 
function addPoint() {
 
function addPoint() {

Latest revision as of 17:20, 20 February 2013

Constructs a polynomial of degree [math]n[/math] through [math]n+1[/math] given points. Points can be added by clicking on "Add point". The dotted line is the graph of the first derivative, the dashed line is the graph of the second derivative.

References

The underlying JavaScript code

var board = JXG.JSXGraph.initBoard('box', {boundingbox: [-5, 10, 7, -6], axis: true});

var p = [];
p[0] = board.create('point', [-1,2], {size:4});
p[1] = board.create('point', [3,-1], {size:4});
var f = JXG.Math.Numerics.lagrangePolynomial(p);
var graph = board.create('functiongraph', [f,-10, 10], {strokeWidth:3});
var d1 = board.create('functiongraph', [JXG.Math.Numerics.D(f), -10, 10], {dash:1});
var d2 = board.create('functiongraph', [JXG.Math.Numerics.D(JXG.Math.Numerics.D(f)), -10, 10], {dash:2});

function addPoint() {
    p.push(board.create('point',[(Math.random()-0.5)*10,(Math.random()-0.5)*3],{size:4}));
    board.update();
}