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# Bernoulli's Method

In order to find a root of a polynomial equation

 (1)

consider the difference equation

 (2)

which is known to have solution

 (3)

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

Root

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## References

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.

## Referenced on Wolfram|Alpha

Bernoulli's Method

## Cite this as:

Weisstein, Eric W. "Bernoulli's Method." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BernoullisMethod.html