MATH6800/CSCI6800 Computational Linear Algebra

Homework 2.

Due: Monday, September 25, 2000.

1.

Demmel, Question 2.1.

2.

Demmel, Question 2.9. Note: This question assumes you can use exact arithmetic throughout.

3.

Demmel, Question 2.13. Note:

• To show that a given formula for M^-1 is really the inverse of M, you only need to verify that the product M M^-1 (or M^-1M) is equal to the identity matrix.
• In parts 2 and 3, suppose that you have already done Gaussian elimination on A to get its L and U factors, so solving Ax=b is fast (costs just O(n²)). Exploit this to solve By=c in O(n²), rather than O(n³), which is what Gaussian elimination on B would cost.

4.

You have a choice:

Either:

Demmel, Question 2.14
Note: The FORTRAN version of LAPACK is installed on RCS in /campus/math/lapack. You can link to it by -L/campus/math/2.0/@sys/lib -llapack, or find the source in /campus/math/lapack/2.0/distrib/SRC.
If you choose this option, you can also OMIT one of questions 2.9, 2.13, or 2.18.

Or:

Demmel, Questions 2.17 AND 2.20.

5.

Demmel, Question 2.18.

	John Mitchell
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