On the Convergence of Cyclic Jacobi Methods

In a cyclic Jacobi method for calculating the eigenvalues andeigenvectors of a symmetric matrix, the pivots are chosen inany fixed cyclic order. It is not known in theory whether convergenceto the solution is always obtained, although convergence hasbeen proved subject to a restriction on the angle of rotationabout each pivot (Henrici, 1958). Now we report an actual computercalculation where a cyclic Jacobi method failed, due to computerrounding errors, so in practice the angle restriction may beneeded. A new bound for the angle restriction is given thatis less severe than the one proposed originally.