Exactly. It is just a description bug. Krylov accumulates vectors A^i x and uses them directly.
Lanczos kind of does the Gram-Schmidt thing on the fly as you say and is also cleverly able to use the bi or tri diagonal matrix of coefficients for a very efficent way of finding the eigenvalues. I suspected you had it right because you mentioned the tri-diagonal matrix. On Sun, Feb 21, 2010 at 9:58 PM, Jake Mannix <jake.man...@gmail.com> wrote: > I guess I should say on the wiki that after every iteration, the part > orthogonal to the current basis is subtracted off, so you always continue > to generate an > expanding basis, if that detail is what helps distinguish Krylov iteration > (I've never > seen raw Krylov described as a full algorithm anywhere, just as a > "concept") from > Lanczos. > -- Ted Dunning, CTO DeepDyve
