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M. Stewart and P. Van Dooren
performed. Each time a right rotation is performed and V2 is updated, a corresponding
right rotation is performed on P and S. The rotation performed on P destroys the
QR
decomposition of P. Since all of the right rotations which are used to update the generalized
UI~V decomposition operate on adjacent columns, there are clearly three ways in which the
QR decomposition can be damaged. The simplest is when the update to V2 only affects one
of the matrices V23, V24, or V25. In this case the rotation operates on two adjacent columns
of P and hence merely creates a single ...