## Mathematics, Department of

#### Date of this Version

1926

#### Abstract

*Approximation to the Least Root of a Cubic* Bernoulli's method of approximating the largest root of an equation

(1) *x*^{3} = *ax*^{2} + *bx* + *c*,

with real coefficients, is to use (1) as a scale of relation for the recursion formula *A*_{n} = *a**A*_{n-1} + *bA*_{n-2} + *cA*_{n-3}. Successive *A*’s are calculated starting from any initial values. Then *A*_{n+i}/*A*_{n} for increasing values of *n* approximates that root of (1) which has the greatest absolute value if that root is real. The method here given for approximating the least root of (1) is similar to Bernoulli's.

## Comments

Published in

Bull. Amer. Math. Soc.32 (1926) 263-268.