Related papers: A fast algorithm for the inversion of Abel's trans…
We extend the usual projective Abel-Radon transform to the larger context of a smooth complete toric variety X. We define and study toric concavity attached to an algebraic splitting vector bundle on X and we prove a toric version of the…
Unknown unitary inversion is a fundamental primitive in quantum computing and physics. Although recent work has demonstrated that quantum algorithms can invert arbitrary unknown unitaries without accessing their classical descriptions,…
We present a new primitive for quantum algorithms that implements a discrete Hermite transform efficiently, in time that depends logarithmically in both the dimension and the inverse of the allowable error. This transform, which maps basis…
We prove an inversion theorem for the Fourier transform defined for normal functions, in the case when such functions are of moderate decrease, and in dimensions 2 and 3. This improves on Carleson's general almost everywhere convergence…
We present an efficient and very flexible numerical fast Fourier-Laplace transform, that extends the logarithmic Fourier transform (LFT) introduced by Haines and Jones [Geophys. J. Int. 92(1):171 (1988)] for functions varying over many…
New high statistics data from the second generation of ultrarelativistic heavy-ion experiments open up new possibilities in terms of data analysis. To fully utilize the potential we propose to analyze the $m_\perp$-spectra of hadrons using…
We present the 2-point function from Fast and Accurate Spherical Bessel Transformation (2-FAST) algorithm for a fast and accurate computation of integrals involving one or two spherical Bessel functions. These types of integrals occur when…
Various applications such as MRI, solution of PDEs, etc. need to perform an inverse nonequispaced fast Fourier transform (NFFT), i. e., compute $M$ Fourier coefficients from given $N$ nonequispaced data. In the present paper we consider…
This paper introduces the theory and hardware implementation of two new algorithms for computing a single component of the discrete Fourier transform. In terms of multiplicative complexity, both algorithms are more efficient, in general,…
In this paper, we first present an explicit expression for the inverse\emph{} of a type of matrices. As special applications, the inverse of some matrices arising from implicit time integration techniques, such as the well-known implicit…
The ability to efficiently infer system parameters is essential in any signal-processing task that requires fast operation. Dealing with quantum systems, a serious challenge arises due to substantial growth of the underlying Hilbert space…
The Laplace transform is a useful and powerful analytic tool with applications to several areas of applied mathematics, including differential equations, probability and statistics. Similarly to the inversion of the Fourier transform,…
In this article, we present an $O(N \log N)$ rapidly convergent algorithm for the numerical approximation of the convolution integral with radially symmetric weakly singular kernels and compactly supported densities. To achieve the reduced…
The semivarying coefficient models are widely used in the application of finance, economics, medical science and many other areas. The functional coefficients are commonly estimated by local smoothing methods, e.g. local linear estimator.…
We show that the quantum Fourier transform on finite fields used to solve query problems is a special case of the usual quantum Fourier transform on finite abelian groups. We show that the control/target inversion property holds in general.…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
We recast homogeneous linear recurrence sequences with fixed coefficients in terms of partial Bell polynomials, and use their properties to obtain various combinatorial identities and multifold convolution formulas. Our approach relies on a…
We present a quantum algorithm to compute the discrete Legendre-Fenchel transform. Given access to a convex function evaluated at $N$ points, the algorithm outputs a quantum-mechanical representation of its corresponding discrete…
Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and…
Index transforms with the product of the associated Legendre functions are introduced. Mapping properties are investigated in the Lebesgue spaces. Inversion formulas are proved. The results are applied to solve a boundary value problem in a…