Math 164 - quiz three - what is your approximation for the

Question

Quiz Three

Show steps, use no notes or advanced calculator functions.

Let

A =	3	2
	2	3

1.  Perform two iterations of the Power Method (PM) using the initial guess

v =	1
	0

What is your approximation for the largest eigenvalue?

2. Perform one iteration of the Inverse Power Method (IPM) using the initial guess

v =	1
	0

v = ( 1 ). What is your approximation for the smallest eigenvalue?

3. Verify that

v =	1
	1

is an eigenvector corresponding to the largest eigenvalue. Use this information to approximate the eigenvector conesponding to the smallest eigenvalue by performing one iteration of the PM with deflation. How accuarate is your eigenvector approximation?

4. Pseudocode a tridiagonal Gaussian elimination solver, given as input vectors D, U, L, and b corresponding to the diagonal, upper and lower diagonals, and the right hand side (RHS).