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On the Newton-Raphson method of Approximation

Published online by Cambridge University Press:  31 October 2008

H. W. Richmond
H. W. Richmond
Affiliation:
King's College, Cambridge.
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The Method.—An equation F(x) = 0 has, a root x = r, not known exactly. From a first approximation to r, x = a, a second approximation, x = b, is obtained from the formula

From b a third approximation, x = c, is obtained by the same formula, and so on. The method is pointless unless the successive approximations do actually tend to r; a rule that ensures this is due to Fourier.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 34 , January 1944 , pp. 5 - 8
Copyright
Copyright © Edinburgh Mathematical Society 1944

References

1 Oeuvres, , Vol. 2, pp. 243–253.Google Scholar