QUOTIENT - DIFFERENCE TYPE GENERALIZAnONS OF THE POWER METHOD AND THEIR ANALYSIS

The recursion relations tha~ were proposed in [2] for implementing vector extrapolation methods are 'used for devising generali}:3tions of the power method for linear operators. These generalizations are shown to produce approximatioQS to largest eigenval'ues of a linear operator under certain conditions. They are similar in fonn to. the quotient-difference algorithm and share similar convergence properties with the latter. These convergence properties resemble also those obtained for the basic LR~ and QR algorithms. Finally, it is shown that the convergence rate produced by one of these generalizations is twice as fast for nonnal operators as it is for non-nonnal operators. T ec hn io n C om pu te r Sc ie nc e D ep ar tm en t T eh ni ca l R ep or t C S0 54 5 19 89