Homework #5 Due 11-11-98

(1) Work p 121; 19

(2) Use Neville's Method to approximate e^2.5 with the values:

Determine Q_3,2

(3) You are to fit a natural spline s(x) to the function f(x) given the following information:

xk	0	1	2
f(xk)	1		0

(a) Using the spline s(x), approximate f(.3) and f(1.4)

(b) Evaluate .

(4) You are given the following data: f(0) = 0.00, f(1) = 0.10, f(2) = 0.75, f(3) = 0.95. Let A be the estimate for f(1.5) determined from the interpolating polynomial using the nodes 0, 1, and 2. Let B be the estimate for f(1.5) determined from the interpolating polynomial using the nodes 0, 1, 2, and 3. Determine A - B.

(5) Work p 155, 7 (Hint: Use the conditions stated in Definition 3.10 on p 144)

(6) Work p 155, 11 (Hint: Use Theorem 3.11). You will set up a system of linear equations which you must solve. Since the number of unknowns are > 2, you might want to use an HP calculator, Derive, PC-Matlab (Read Matlab remarks below) or some other software to solve them. In any event, exhibit all the linear equations. To find f'(0.5), be sure to exhibit f'(x) for x's near 0.5 which will require using the coefficients you found earlier. The finding of f''(0.5) is similar.

Solving a system of linear equations via Matlab .

To solve 2x - 3y = -4, x + y = 3. This can be interpreted as ax = b. Use the following matlab code.

a=[2 -3; 1 1]

b=[-4;3]

x=a\b

x is the solution