On the quadratic convergence of the Jacobi method for normal matrices
George D. Loizou · The Computer Journal · 1972
In this paper it is proved that the Jacobi method for normal matrices, due to Goldstine and Horwitz, after a certain stage in the process, is quadratically convergent. The pivot pair (p, q) is chosen so that the sum of the absolute squares of the elements in positions (p, q) and (q, p) is greatest. In this respect, the results obtained here supplement those of Ruhe who considered only the special row cyclic method of enumerating pivot elements.