Homework #6 Due 11-18-98

(1) p 157; 27. In a, I simply want graphs. Work a in either of the 2 following ways.

Use my spline.exe from

ftp://www.etsu.edu/kerleyl/

to obtain a file containing points for plotting the 2 spline curve approximations for the two samples. This will require your constructing 2 data files for 2 samples and running spline.exe 2 times. Then apply appropriate software to obtain 2 graphs from the 2 data files

OR

Use PC-Matlab to obtain the 2 plots.

To work part b, run my spline.exe and from the output files you generate containing the coefficients, pick off the appropriate ai,bi,ci, and di. That is, for (x,ymax) , x lies in some [x_i,x_i+1)) for some i. This may require your studying part a. Then determine the maximum of a_i + b_i(x-x_i) + c_i(x-x_i)^2 + d_i(x-x_i)^3 on [x_i,x_i+1) via calculus (if necessary).

CAUTION: The algorithm in spline.exe based on the book gives slightly different results than the one in PC-Matlab. Apparently PC-Matlab has refined the one in our text.

(1) p 177; 3a, 4a

(2) p 197: 1b, 2b, 3b

(3) p 205; 1a, 2a