The Joint Bidiagonalization Method for Large GSVD Computations in Finite Precision

The joint bidiagonalization (JBD) method has been used to compute some extreme generalized singular values and vectors of a large regular matrix pair . We make numerical analysis the underlying JBD process establish relationships between it two mathematically equivalent Lanczos bidiagonalizations in finite precision. Based on results analysis, we investigate convergence approximate show that, under mild conditions, semiorthogonality Lanczos-type suffices deliver with same accuracy as full orthogonality does, meaning that is only necessary seek for efficient semiorthogonalization strategies process. sharp bound residual norm an value corresponding right vectors, which can reliably estimate without explicitly computing before occurs.