Yousef Saad Department Of Computer Science And Engineering

IR: Use of the Lanczos algorithm (1)
➤ Let A ∈ R m×n . Apply the Lanczos procedure to M =
AA T . Result:
Q T k AAT Qk = Tk
with Qk orthogonal, Tk tridiagonal.
➤ Define si ≡ orth. projection of Ab on subspace span{Qi}
si := QiQ T i Ab.
➤ si can be easily updated from si−1:
si = si−1 + qiq T
i Ab.
CSE Colloquium 11/09/09 p. 49