ON THE CONDITION BEHAVIOR IN THE JACOBI METHOD

The aim of this note is to show that the matrix S(n, alpha) = (1 - alp ha)I + alpha ee(tau), e = (1,...,1)(tau), alpha is an element of (0, 1 ) is not a counterexample for the accuracy properties of the Jacobi me thod for computing the singular and eigenvalue decomposition, as might be understood from a recent article of Mascarenhas in this journal. I n fact, the Jacobi process on S(n, alpha) is an example of the perfect behaviour of the algorithm. It is shown that Jacobi rotations preserv e the optimal (with respect to diagonal scalings) spectral condition n umber of S(n, alpha).