The hybrid weighted diaphony
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In this book the hybrid weighted diaphony as a measure for the irregularity of distribution of sequences is introduced. The computing complexity of the hybrid weighted diaphony is shown. A function class which is a reproducing kernel Hilbert space is introduced and a formula for the worst-case error of the quasi-Monte Carlo integration in this space is given. It is shown that the worst-case error and the hybrid weighted diaphony of the net of nodes of the integration with exactness of multiplicative constant are equal. An inequality of the type of Erdos-Turan-Koksma for the hybrid weighted dia...
In this book the hybrid weighted diaphony as a measure for the irregularity of distribution of sequences is introduced. The computing complexity of the hybrid weighted diaphony is shown. A function class which is a reproducing kernel Hilbert space is introduced and a formula for the worst-case error of the quasi-Monte Carlo integration in this space is given. It is shown that the worst-case error and the hybrid weighted diaphony of the net of nodes of the integration with exactness of multiplicative constant are equal. An inequality of the type of Erdos-Turan-Koksma for the hybrid weighted diaphony of an arbitrary net is shown.
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