Abstract
This chapter consists of three sections— the first focusing on a method for downdating ULV decomposition along with its main results. The second section presents an error analysis showing the favorable stability properties of this downdating algorithm and the procedures carried out to develop it. The third section describes the ULV decomposition algorithm in detail. The ULV method was described by Stewart who also gives a method for updating it. It is a particular case of what Lawson and Hanson called HRK decompositions but the difference is that blocks that are exactly zero are separated out. The downdating algorithm presented here coupled with Stewart's updating algorithm show that the ULV decomposition can be updated and downdated in O(n2) flops in a manner that preserves their structure.
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