Assignment 2 of course numerical linear algebra
Exercise 1: Show the code for LanczosCGS(A,v,k)
Exercise 2: Take A = diag([0:10]) and v = ones(11,1) and run LanczosCGS(A,v,10) Next take v = [1;2;2^2;2^3;2^4;2^5;2^6;2^7;2^8;2^9;2^10] and run LanczosCGS(A,v,10) Comment on the differences
Exercise 3:
Exercise 4: Show the code [] Play the movie of two frames per second with starting vector v=ones() What is your opinion on the convergence properties of the Ritz values in this notorious example?
Exercise 5: Show the code [] Show the 10 plots. What do these plots tell you about the potential success of eigenvalue algorithms that try to approximate eigenvalues of G, and of Arnoldi in particular?
Exercise 6:
Show the proof of theorem
Proof is similar to
Exercise 7: Show code FilterAway(mu,V,H) Show code [V,H] = ExtendArnoldi(A,V,H) Show the code L = ListRitzData(H) Confirm result of exercise 6
Exercise 8: Show the implementation of extend, filter and exit.
Exercise 9:
Exercise 10: Show code [V,H] = FilterAway2(mu,V,H)