MATH6800/CSCI6800 Computational Linear Algebra

Homework 3.

Due: Tuesday, October 10, 2000.
Due: Thursday, October 12, 2000.

1.

Demmel, Question 3.1.

2.

Demmel, Question 3.4. Note: the "previous question" is the weighted least squares problem of minimizing the norm of D(Ax-b).

3.

Demmel, Question 3.6.

4.

Demmel, Question 3.18.

• Hint: If you know the method of Lagrange, or the Karush-Kuhn-Tucker optimality conditions, you can use those.
• Alternative hint: Let $\bar{x}$ be any solution to Cx=d. We are going to keep $\bar{x}$ fixed. Let the columns of the matrix W form a basis for the nullspace of C. Then the set of points satisfying Cx=d is the set of points of the form $\bar{x}+Wy$ for some vector y.

	John Mitchell
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