Pricing longevity derivatives via Fourier transforms

Pricing Asian options via Fourier and Laplace transforms

Faster Fourier Transforms via Automatic Program Specialization

Because of its wide applicability many e cient implementations of the Fast Fourier Transform have been developed We propose that an e cient implemen tation can be produced automatically and reliably by partial evaluation Partial evaluation of an unoptimized implementation produces a speedup of over times The automatically generated result of partial evaluation has performance com parable to or ...

Faster Polynomial Multiplication via Discrete Fourier Transforms

We study the complexity of polynomial multiplication over arbitrary fields. We present a unified approach that generalizes all known asymptotically fastest algorithms for this problem. In particular, the well-known algorithm for multiplication of polynomials over fields supporting DFTs of large smooth orders, Schönhage-Strassen’s algorithm over arbitrary fields of characteristic different from ...

Approximate fast graph Fourier transforms via multi-layer sparse approximations

The Fast Fourier Transform (FFT) is an algorithm of paramount importance in signal processing as it allows to apply the Fourier transform in O(n logn) instead of O(n) arithmetic operations. Graph Signal Processing (GSP) is a recent research domain that generalizes classical signal processing tools, such as the Fourier transform, to situations where the signal domain is given by any arbitrary gr...

Fast Computation of Voigt Functions via Fourier Transforms

This work presents a method of computing Voigt functions and their derivatives, to high accuracy, on a uniform grid. It is based on an adaptation of Fourier-transform based convolution. The relative error of the result decreases as the fourth power of the computational effort. Because of its use of highly vectorizable operations for its core, it can be implemented very efficiently in scripting ...