The calculation of certain Bessel functions

Abstract

4. Conclusions. This method appears to be attractive for use in the problem of calculating all eigenvalues and a complete set of orthonormalized eigenvectors for the following reasons: (a) Like the cyclic threshold Jacobi method, there is no search for largest pivotal elements. (b) Unlike the cyclic threshold Jacobi method there is no limitation on the angle of rotation in the Jacobi rotation as Forsythe and Henrici (1) showed was necessary for convergence. (c) Each iteration creates n 1 zeros at the cost of 3 square roots as compared to one zero in the Jacobi method at the cost of 2 square roots.