A uniform distribution question related to numerical analysis
Harald Niederreiter and Charles F. Osgood
Math. Comp. 30 (1976), 366-370
Primary 65D30; Secondary 10K05
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Abstract: Using the theory of uniform distribution modulo one, it is shown that under certain conditions on the real-valued functions and on [0,1 ], where and x denotes the fractional part of x. The conditions are as follows: exists for all but finitely many points in [0, 1], changes sign at most finitely often, and is bounded away in absolute value from both 0 and , whereas is of bounded variation on [0,1]. Also, under these conditions on , These results, which are, in fact, deduced from somewhat more general propositions, answer questions of Feldstein connected with discretization methods for differential equations.
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E. W. HOBSON, The Theory of Functions of a Real Variable and the Theory of Fourier's Series, Vol. I, 3rd ed., Cambridge Univ. Press, London, 1927.
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Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974.
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Duke Math. J. 40 (1973), 633–649. MR 0337873
G. van der Corput, Zahlentheoretische Abschätzungen,
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