Do rate, if you liked it! Sorry for upside down, and the idea was to keep it simple and do as clear an intro as possible. Youtube limits me to 10 minutes also.
Good question! They are not the eigenvalues and eigenvectors of A, but of a projection of A onto the Krylov subspace because of the orthogonalization. However, the largest eigenvalues are an approximation of A also.
I like your teaching, but can you do a longer version of it and have it right-side up instead of up-side down? Also, after you get orthogonal vectors from each iteration q1....qn , are these then the eigenvectors? Do they correspond to the eigenvalues in some order (is q1 the eigenvector corresponding to the largest eigenvalue)? Thanks for putting this up!
Do rate, if you liked it! Sorry for upside down, and the idea was to keep it simple and do as clear an intro as possible. Youtube limits me to 10 minutes also.
fierce10 2 years ago
Good question! They are not the eigenvalues and eigenvectors of A, but of a projection of A onto the Krylov subspace because of the orthogonalization. However, the largest eigenvalues are an approximation of A also.
fierce10 2 years ago
I like your teaching, but can you do a longer version of it and have it right-side up instead of up-side down? Also, after you get orthogonal vectors from each iteration q1....qn , are these then the eigenvectors? Do they correspond to the eigenvalues in some order (is q1 the eigenvector corresponding to the largest eigenvalue)? Thanks for putting this up!
frank0lin 2 years ago