Bernoulli's Method

In order to find a root of a polynomial equation


consider the difference equation


which is known to have solution


where w_1, w_2, ..., are arbitrary functions of t with period 1, and x_1, ..., x_n are roots of (1). In order to find the absolutely greatest root (1), take any arbitrary values for y(0), y(1), ..., y(n-1). By repeated application of (2), calculate in succession the values y(n), y(n+1), y(n+2), .... Then the ratio of two successive members of this sequence tends in general to a limit, which is the absolutely greatest root of (1).

See also


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Whittaker, E. T. and Robinson, G. "A Method of Daniel Bernoulli." §52 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 98-99, 1967.

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Bernoulli's Method

Cite this as:

Weisstein, Eric W. "Bernoulli's Method." From MathWorld--A Wolfram Web Resource.

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