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On the Danilewski method for computing the characteristic polynomial

Eldon Hansen

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Abstract

The Danilewski method, as commonly applied, tends to be a very unstable method for finding the characteristic polynomial of a matrix. In this paper we show that, by an appropriate computational procedure, the method seems, in general, to be relatively stable. For the examples tried, it has yielded the characteristic polynomial with high accuracy.

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The Danilewski method, as commonly applied, tends to be a very unstable method for finding the characteristic polynomial of a matrix. In this paper we show that, by an appropriate computational procedure, the method seems, in general, to be relatively stable. For the examples tried, it has yielded the characteristic polynomial with high accuracy.

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Available abstract

The Danilewski method, as commonly applied, tends to be a very unstable method for finding the characteristic polynomial of a matrix. In this paper we show that, by an appropriate computational procedure, the method seems, in general, to be relatively stable. For the examples tried, it has yielded the characteristic polynomial with high accuracy.

Key concepts: Matrix polynomial, Polynomial, Characteristic polynomial, Polynomial matrix, Computer science, Wilkinson's polynomial, Stable polynomial, Computational complexity theory

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