CONDITION NUMBER AND BACKWARD ERROR FOR THE GENERALIZED SINGULAR VALUE DECOMPOSITION.

Let A,B be two matrices having the same number of columns, and let (AT,BT)T have full column rank. Certain normwise condition numbers for a finite generalized singular value (GSV) of the matrix pair {A,B} are defined, and explicit expressions of the condition numbers for a simple, nonzero GSV are derived. Moreover, a normwise backward error of {A,B} with respect to an approximate GSV and an associated approximate generalized singular vector group is also defined, and a computable formula of the backward error is obtained. The results are illustrated by numerical examples. [ABSTRACT FROM AUTHOR]