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A Note on a Formula of Newton and an Extension Thereto

Published online by Cambridge University Press:  27 November 2014

H. L. Garfath
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Extract

Let f(x), f″(x), f″(x) denote a function of x, its first and second derivatives respectively. If f(x), f″(x) are one-valued, finite and continuous, and f″(x) exists in the neighbourhood of the value a of x, then

where o < θ < I. Suppose the value a is an approximation to a root of the equation f(x) = o, the true value of which is a + h. Equation (I) becomes

and supposing that f″(a) ≠ o

that is, a + h differs from .

Type
Research Article
Information
Journal of the Staple Inn Actuarial Society , Volume 6 , Issue 2 , October 1946 , pp. 63 - 66
Copyright
Copyright © Institute of Actuaries Students' Society 1946

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