NLA-Assignment-2

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)