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 Demboʹs (1988) upper bound as a special case. Then we derive the kth-order upper bound (lambda)/sub k/ and its first-round iteration (lambda)/sub k//sup (1)/ which is much tighter than the Demboʹs upper bound (lambda)/sub 0/.