Math 477 — Homework Assignment 3, due Oct.12, 2006
1. Consider the matrices
A=
1 0
0 1
1 0
, B =
1 2
0 1
1 0
used on the previous homework.
(a) Using any method you like, determine (on paper) a reduced QR factorization A=ˆ
Qˆ
Rand
a full QR factorization A=QR.
(b) Again using any method you like, determine reduced and full QR factorizations B=ˆ
Qˆ
R
and B=QR.
2. Apply the Gram-Schmidt process (on paper) to the three vectors [3,4,0]T, [1,1,1]T, and [1,2,0]T.
3. Let Abe an m×nmatrix. Determine the exact number of floating point additions, subtractions,
multiplications and divisions involved in performing the classical and modified Gram-Schmidt
algorithms as listed in the classnotes.
