A Robust Criterion for the Modified Gram--Schmidt Algorithm with Selective Reorthogonalization
Luc Giraud, Julien Langou · SIAM Journal on Scientific Computing · 2003
A new criterion for selective reorthogonalization in the modified Gram--Schmidt algorithm is proposed. We study its behavior in the presence of rounding errors. We give some counterexample matrices which prove that the standard criteria might fail. Through numerical experiments, we illustrate that our new criterion seems to be suitable also for the classical Gram--Schmidt algorithm with selective reorthogonalization.