Math 151A Homework #6
1. Hermite interpolation
Find a polynomial approximation to the function f(x) = log(x) using the value of f(x) at
x0= 1 and x1=e, and the derivative of f(x) at x0. Plot your answer.
2. numerical differentiation
Given the data in the following table, compute a 3-point approximation to the derivative at
each of the points.
x f(x)
0 1
1 2
2 5
3. error for numerical differentiation
Compute an error bound for using a 3-point centered difference formula to compute the
second derivative of f(x) = sin(x) using the points xk= 0, π/8, π/4.
4. Richardson’s extrapolation
Suppose N(h) is an approximation to Msuch that
M=N(h) + K2h2+K4h4+K6h6+· · ·
where Kjis constant. Use the values N(h), N(h/3), and N(h/9) to produce an order h6
approximation to M.