On the Danilewski Method

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Abstract
In this paper we describe a computational procedure for the Danilewski method which employs a "search for pivots." It yields the characteristic poly- i: } nomiM much more accurately than the procedures reported by previous investigators. We shall then present a count of mathematical operations used in applying the method with multiple precision arithmetic. These operation counts emphasize the well-known fact that the method is quite fast. We then conclude that the } method should not be regarded as an uneconomical process for obtaining matrix eigenvalues.