Scientific Computing

This modules illustrates Newton interpolation. For an ordered set
of points *t*_{i},
*y*_{i})*i* =
1,…,*n**j*-th Newton basis function is
given by *π*_{j} (*t*)*t* − *t*_{1}) · · ·
(*t* − *t*_{j−1})

First the user selects a set of data points by clicking either
*Choose Random Points* to generate all the points randomly, or
*Choose Specific Points* to specify points individually. In the
latter case, the user clicks on the graph to indicate the locations of
the points. To prevent points from being too close to each other, they
may not be chosen in the shaded buffer zone surrounding existing
points. After the set of data points has been chosen, the user clicks
*Apply* to have them take effect. Now the user clicks on the
points one at a time in any desired order to build the Newton
interpolant incrementally. As each point is clicked, the plotted
interpolant changes to include the new point, and the resulting
polynomical is expressed below as a linear combination of the Newton
basis functions. At any time during this process, *Reset
Interpolant* clears the interpolant while retaining the current set
of points. By resetting the interpolant, the user can observe that the
final interpolant is independent of the order in which the points are
selected.

**Reference:** Michael T. Heath, *Scientific Computing,
An Introductory Survey*, 2nd edition, McGraw-Hill, New York,
2002. See Section 7.3.3, especially Example 7.4.

**Developers:** Evan VanderZee and Michael Heath