Abstract
obtain a sequence of bounds for p(A ) in terms of p(f A' I) (r = 1, 2, ) which are less than or equal to p( l A j) and converge to p(A ). In this manner we are partially accounting for the effect on p(A) of the phases of the ai,. In Section II we derive bounds for p(A) in terms of the Frobenius norm of A. These bounds always lie in the field of values of A, are computationally well suited to complex matrices and can be used in conjunction with the techniques of Section I. The authors are indebted to Olga Taussky and Alston Householder for suggestions.
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