On Fri, Feb 7, 2020 at 1:43 PM Victor Eijkhout <[email protected]> wrote:
> > > On , 2020Feb7, at 12:31, Mark Adams <[email protected]> wrote: > > BTW, one of my earliest talks, in grad school before I had any real > results, was called "condition number does not matter” > > > After you learn that the condition number gives an _upper_bound_ on the > number of iterations, you learn that if a few eigenvalues are separated > from a cluster of other eigenvalues, your number of iterations is 1 for > each separated one, and then a bound based on the remaining cluster. > This is _only_ for normal matrices. Not true for general matrices. Matt > (Condition number predicts a number of iterations based on Chebychev > polynomials. Since the CG polynomials are optimal, they are at least as > good as Chebychev. Hence the number of iterations is at most what you got > from Chebychev, which is the condition number bound.) > > Victor. > > > -- What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead. -- Norbert Wiener https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
