Verification algorithms for generalized singular values

By means of interval arithmetic tools we present new algorithms for verifyi ng and enclosing generalized singular values and corresponding vectors for a matrix-pair (A, B) is an element of R-pxn x R-qxn. To this end, we state and prove a fundamental theorem in interval analysis which shows a way how enclosures can be constructed if approximations are known. Furthermore, we perform a careful comparison of the new method with those introduced in [11 ].