INSTRUCTOR 
Prof. Andrew Knyazev
Office: CU (Dravo) 620G. Phone: 556-8102.
Office hours: Tue 3pm - 6pm

NA II       EXAM #1     (Chapters 6-7)        Mon Feb 5 1996
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1. Suppose that a 3x3 tridiagonal matrix is already
in a reduced (upper-triangular) form with elements d(1), d(2), d(3) 
on the main diagonal and with elements c(1), c(2) on another diagonal,
and right-hand side b(1), b(2), b(3).
Find all mistakes in the following algorithm
of the back substitution:

for i=1 to 3 step 1
 x(i) = ( b(i) - c(i) x(i-1) ) / b(i)
end do 


2. Perform the forward Gaussian elimination,  
using scaled partial pivoting, for the system 

  1 -2  x   1
 -2  0  x   8 

3. Use knots -1, 0, and 1 and function f(x)= x
Find the first-degree interpolation spline.

       
4. Use knots -1, 0, and 1 and function f(x)= x
Find the second-degree interpolation spline with z  = 1.