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arXiv · 2307.15754

A fast procedure for the construction of quadrature formulas for bandlimited functions

Abinand Gopal·Vladimir Rokhlin
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Abstract

We introduce an efficient scheme for the construction of quadrature rules for bandlimited functions. While the scheme is predominantly based on well-known facts about prolate spheroidal wave functions of order zero, it has the asymptotic CPU time estimate $O(n log n)$ to construct an n-point quadrature rule. Moreover, the size of the ``$n log n$'' term in the CPU time estimate is small, so for all practical purposes the CPU time cost is proportional to $n$. The performance of the algorithm is illustrated by several numerical examples.

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Abinand Gopal, Vladimir Rokhlin. 2023-07-28. A fast procedure for the construction of quadrature formulas for bandlimited functions. https://arxiv.org/abs/2307.15754

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