Analysis of Algorithms for Orthogonalizing Products of Unitary Matrices

✍ Scribed by Roy Mathias

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 995 KB
• Volume: 3
• Category: Article
• ISSN: 1070-5325
• DOI: 10.1002/(sici)1099-1506(199603/04)3:2<125::aid-nla72>3.0.co;2-8

✦ Synopsis

We consider the problem of computing u k = Qk uk-1 (where U0 is given) in finite precision (CM = machine precision) where U0 and the Qi are known to be unitary. The problem is that fik, the computed product may not be unitary, so one applies an O(n2) orthogonalizing step after each multiplication to (a) prevent fik from drifting too far from the set of unitary matrices (b) prevent fik from drifting too far from Uk the true product.

Our main results are 1. Scaling the rows to have unit length after each multiplication (the cheapest of the algorithms considered) is usually as good as any other method with respect to either of the criteria (a) or @).

2. A new orthogonalization algorithm that guarantees that the distance of fik (k = 1,2, . . .) to the set of unitary matrices is bounded by n 3 . 5 c ~ for any choice of Q i .