In this paper the complexity of the local solution of Fredholm integral equations is studied. For certain Sobolev classes of multivariate periodic functions with dominating mixed derivative we prove matching lower and upper bounds. The lower bound is shown using relations to s-numbers. The upper bound is proved in a constructive way providing an implementable algorithm of optimal order based on...

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This paper proposes an efficient memory-based radix-2 FFT architecture, which greatly improves the memorybased FFT [5], [6] by reducing 50% memory size requirement, while maintaining a simple address generator. Specifically the memory size is reduced to 1.25N words. In addition, the multiplier utilization rate is 100%.

In a recent paper, M. B. Nathanson [Nathanson] finds the highest order term of the asymptotic formula for the number of partitions with parts in a finite set. This is done without referring to the partial fraction expansion of the generating function. In this paper, we essentially find the entire asymptotic formula without using partial fractions. This is done by the “metaphysical method” descr...

We show that the multiple zeta sum: ζ(s1, s2, ..., sd) = ∑ n1>n2>...>nd 1 n1 1 n s2 2 ...n sd d , for positive integers si with s1 > 1, can always be written as a finite sum of products of rapidly convergent series. Perhaps surprisingly, one may develop fast summation algorithms of such efficiency that the overall complexity can be brought down essentially to that of one-dimensional summation. ...