MATH 6664 and C SC 5646: Numerical Linear Algebra
Spring 1997. University of Colorado at Denver


HOURS: TR 5:30-6:45 pm, CN 223

INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo) 644. Phone: 556-8102.
Office hours: Wed 3pm - 6pm (or by appointment)
WWW: http://www-math.cudenver.edu/~aknyazev
Email: aknyazev@math.cudenver.edu

TEXTBOOK:
Iterative Solution Methods. Owe Axelsson. Cambridge University Press, 1994.

Final. Due May 13, 1997, 10am.

Let A be a given real symmertic positive definite matrix, v be a given real vector,
F(x) be the following function

F(x)=(Ax,x)/(x,x)

where x is an arbitary nonzero real vector.

(a) Find an explicit formula for the grad F(x).
Hint: Use the same approach as in the text, p. 460.

(b) Find an explicit formula for the real scalar c that gives the minimum to F(v-c grad F(v)).
Hint: Consider F(v-c grad F(v))=f(c) as a scalar function of c and find its minimum using the first derivative.


Andrew Knyazev
May 6 13:19:30 MST 1997