Mathematics, Department of


Date of this Version



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


Approximation to the Least Root of a Cubic Bernoulli's method of approximating the largest root of an equation
(1) x3 = ax2 + bx + c,
with real coefficients, is to use (1) as a scale of relation for the recursion formula An = aAn-1 + bAn-2 + cAn-3. Successive A’s are calculated starting from any initial values. Then An+i/An 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.

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