Example 8.6.3.

We adapted the partial reorthogonalization schemes presented in §7.9 for our symmetric indefinite Lanczos implementation. The following table shows that partial reorthogonalization provides substantial, though not dramatic, savings over complete reorthogonalization with comparable accuracy. The time listed in the table is the CPU time spent during the reorthogonalization stage with either the full reorthogonalization strategy or the partial reorthogonalization scheme. The CPU times indicate that complete reorthogonalization is about twice as expensive as partial reorthogonalization in terms of computation.

Model	Speaker	Speaker	Shaft
		(reduced model)
Order $\{A,B\}$	1076	668	800
Lanczos iterations	91	96	110
Number of reorthogonalizations
for semiorthogonality	25	31	40
Reorthogonalization time (partial)	53.7	25.7	46.1
Reorthogonalization time (full)	126.1	53.2	87.0