Aim of the applet
Analyze the Lagrange interpolating polynomial constructed by the nodes.
Input data
By function:
- The function to interpolate.
- Number of nodes of the polynomial.
- Evaluation of the polynomial at a point.
By point table:
- Coordinates of the nodes of the polynomial.
- Number of points of the polynomial.
- Button to represent the polynomial in the graph.
- Evaluation of the polynomial at a point.
By the graph:
- The function and the points can be drag into the graph.
Options menu:
- Boxes to show / hide function, polynomial and grid.
- Number of decimal approximation to the results table.
- Button to put the nodes on your position by default.
- Button to calculate the results table.
Output data
Graph:
- The functon.
- Polynomial P (x) with the nodes passing (Ai).
- Definition of P (x) and an evaluation of this at a point.
Results:
- Table of results.
- No simplified polynomial.
- Simplified polynomial.
Observations
If we are in the "By function", the points are dragged in the domain of the function,
If we are in the "Constructed with", the points are dragged on the all graph.
If you does not enter values for all selected nodes;
It takes a default nodes.
First steps
- Built a interpolating polynomial through three nodes of f (x) = x3-x2 + 2.
How many nodes you need to match the polynomial and function? If you increase the previous number?
- Insert a table with four nodes and calculates the Lagrange polynomial.
Verify that passes through the four nodes.
- Given f(x) = log(x). Calculates a interpolating polynomial using 4 nodes over function.
Increase the number of nodes to see if it improves the approximation of the polynomial.
