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Mathematics of Computation

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Stability of rounded off inverses under iteration


Author: Harold G. Diamond
Journal: Math. Comp. 32 (1978), 227-232
MSC: Primary 65G05
DOI: https://doi.org/10.1090/S0025-5718-1978-0461879-7
MathSciNet review: 0461879
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Abstract: Let f be a monotone and strictly convex (or concave) function on a real interval and let g be the inverse function. Let $ I(x) = x$. For $ \phi $ a real valued function and N a positive integer let $ {\phi _N}(x)$ denote the rounding of $ \phi (x)$ to N significant figures. Let $ h = {g_N} \circ {f_N}$ , the composition of $ {f_N}$ and $ {g_N}$. It is shown that

$\displaystyle h \circ h \circ {I_N} = h \circ h \circ h \circ {I_N},$

and that equality can fail for fewer iterations.

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DOI: https://doi.org/10.1090/S0025-5718-1978-0461879-7
Article copyright: © Copyright 1978 American Mathematical Society