The classical Koksma-Hlawka inequality does not apply to functions with simple discontinuities. Here we state a Koksma-Hlawka type inequality which applies to piecewise smooth functions fχ_{Ω}, with f smooth and Ω a Borel subset of [0,1]^{d}
Brandolini, L., Colzani, L., Gigante, G., Travaglini, G. (2013). On the Koksma-Hlawka Inequality. JOURNAL OF COMPLEXITY, 29(2), 158-172 [10.1016/j.jco.2012.10.003].
On the Koksma-Hlawka Inequality
COLZANI, LEONARDO;TRAVAGLINI, GIANCARLO
2013
Abstract
The classical Koksma-Hlawka inequality does not apply to functions with simple discontinuities. Here we state a Koksma-Hlawka type inequality which applies to piecewise smooth functions fχ_{Ω}, with f smooth and Ω a Borel subset of [0,1]^{d}
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