In recent years several numerical methods have been developed for solving matrix differential systems whose solutions remain on smooth manifolds, such as the orthogonal or symplectic manifold. We consider constant step-size numerical methods for matrix differential systems whose solutions evolve on the manifold of the square oblique rotation matrices OB(n) = {Y R^n×n | diag(Y^TY) = I_n, det(Y) 0}. The theoretical solution of such a differential problem may have inverse of large norm so that several difficulties may arise over its numerical solution. Numerical tests will be reported and the numerical solution of the oblique Procrustes problem will be considered.

MINISIMPOSIUM SESSION: 16. Stability Issues for IVP methods