Condition Number and Backward Error for the Generalized Singular Value Decomposition
Jiguang Sun · SIAM Journal on Matrix Analysis and Applications · 2000
Let A, B be two matrices having the same number of columns, and let (A T , B T ) 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.