Courses   <-  Sean Forman   <-  You Are Here Numerical Analysis

September 30, 2002

Due: October 9, 2002

Assignment#4: (50 points) All work should be your own.

1. (25 pt) Using Maple Worksheet NA_2001-02-13.mws as your guide complete the following exercise. Look at the course website for a pointer to this area.
   1. Without using the computer, find $P_2(x)$ for $f(x) = x^{2/3}$ at $x = 1,8,27$. You do not need to simplify these expressions.

   2. Without using the computer, find $Q_2(x)$ for $f(x) = x^{2/3}$ at $x = 0,1,8$. Note that $Q$ and $P$ are different polynomials because they use different points to approximate the function.

   3. Using Maple or algebra, find the simplified quadratic equations for the above interpolants, $Q$ and $P$.

   4. Using Maple or a calculator, compute the error $f(x) - P_2(x)$ and $f(x) - Q_2(x)$ for $x=0.5$ and $x=12$.

   5. Using Maple, print (or sketch by hand) accurate graphs that compares the error $f(x) - P_2(x)$ and $f(x) - Q_2(x)$ first between $[0,8]$ and then $[1,27]$.

   6. Using complete sentences, state which of the two approximations you would use if you needed to repeatedly evaluate values between $[1,8]$ and why.

2. (5 pt.) 5.2.1

3. (5 pt.) 5.3.8

4. (15 pt.) 5.4.4, Use some linear equation solver to solve the linear equations created in the spline problems. This could be a calculator or maple or some other method.