Written and Programming Assignment
Due:

Tuesday, April 1, 2003, 11AM

1. Written problems chapter 7 Heath text. 7.1, 7.2.

2. Programming Assignment.

This assignment will approximate a function using cubic splines. We will experiment with changing the number of knots and measuring the error in the approximation, for several different functions. The programming and graphing should be done in Matlab for this assignment.

(a) Write a program in Matlab that
takes as input the number **n** = number of equally spaced knots
**k_i
**ina
specified interval **[a,b]**, and function values equal to
**f(k_i)**,
and compute the cubic spline for those knots. (Do not simply call
the spline routine from the toolbox; you must write your own, although
you can use the Matlab routine for help with debugging.) For each
value of **n** from 4 to 50, plot the function and the interpolant over
the interval. To plot the functions, simply evaluate them at several hundred
points in the interval and use the Matlab function
*plot*. Output
the error in both the 2 norm and maximum norm at the midpoint of each interval.

(b) Apply your routines to three different functions

- f(x) = sin(x) on [0, 2 pi],
- f(x) =1/(1 + 25x*x) (Runge's function) on [-1,1], and
- f(x) = sqrt(abs(x-1/e)) on [0,1].

To Hand In:
** ** copy of Matlab code,
written discussion and explanation, sample output, graphs.