Homework due Thursday 3/18

Please come see me or send me e-mail if you're having any problems mathematically, computationally, or otherwise.

Chapter 8

Problems 13, 18, 20, 21, 26, 27, 31, 35 (problem 1 only), 37

Finding Eigenvalues

Look at the diary on finding eigenvalues. Here you construct a 10x10 matrix with known eigenvalues. And then find the largest eigenvalue, iterating until you reach a pre-set tolerance.

Choose three different spectral gaps, lambda_1-lambda_2, and demonstrate that the smaller the gap, the longer it take to reach the tolerance.

For all three cases Demonstrate that the errors are decreasing linearly: error(i+1) <= C*error(i) for some constant C. What is that constant C? Where does it come from?

Demonstrate that you really have found the eigenvector.

Find the second largest eigenvalue and its eigenvector.