The cyclic Jacobi method for computing the principal values of a complex matrix

Abstract

is diagonal (T denotes the transpose), then the main diagonal of A is made up of the numbers Xi in some order. If it is desired to compute the Xi numerically, this result is of no immediate use, since for n> 2 there exists no manageable expression for the general orthogonal matrix of order n. However, Jacobi [6] suggested the computation of the set of Xi as the limiting set of diagonal elements of a sequence of matrices which are generated from A recursively by plane rotations. For k = 0, 1, 2, * *, let ck =cf)k be a real angle and (i, j) = (ik, jk), a pair of integers such that 1 <ik <jk n. The matrix Uk = (upq), where