Modifying Two-Sided Orthogonal Decompositions: Algorithms, Implementation, and Applications.
Peter A. Yoon · 1995
Abstract : In this thesis we propose several algorithms for rank-one updates and downdates to these decompositions with strong stability properties and efficient implementations on high-performance computers. We seek algorithms which only require O(n2) operations per update or downdate unlike recomputing the two-sided orthogonal decomposition (TSOD) in O(n3). We also desire highly regular data movement inherited in these algorithms in order to implement these efficiently on the distributed memory MIMD multiprocessors. The algorithms are based upon 'chasing' strategies for updating and downdating procedures for orthogonal decompositions. (AN)