On determining upper bounds of maximal eigenvalue of Hermitian positive-definite matrix

We first present a new method of determining the upper bounds of maximal eigenvalue of Hermitian positive-definite matrix, which includes the Dembo's (1988) upper bound as a special case. Then we derive the kth-order upper bound /spl Lambda//sub k/ and its first-round iteration /spl Lambda//sub k//sup (1)/ which is much tighter than the Dembo's upper bound /spl Lambda//sub 0/.