Related papers: A new cubature formula with weight functions on th…
Error enhancement properties of data processing algorithms in elementary particle physics measurements are discussed. It is argued that a systematic use of continuous weights instead of hard cuts may reduce errors of the results at the cost…
An index transform, involving the square of Whittaker's function is introduced and investigated. The corresponding inversion formula is established. Particular cases cover index transforms of the Lebedev type with products of the modified…
In this contribution we deal with Gaussian quadrature rules based on orthogonal polynomials associated with a weight function $w(x)= x^{\alpha} e^{-x}$ supported on an interval $(0,z)$, $z>0.$ The modified Chebyshev algorithm is used in…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
The Quantum Fourier Transform offers an interesting way to perform arithmetic operations on a quantum computer. We review existing Quantum Fourier Transform adders and multipliers and propose some modifications that extend their…
This paper introduces a deterministic algorithm for solving an instance of the Subset Sum Problem based on a new method entitled the Bipartite Synthesis Method. The algorithm is described and shown to have worst-case limiting performance…
Weighted model counting computes the sum of the rational-valued weights associated with the satisfying assignments for a Boolean formula, where the weight of an assignment is given by the product of the weights assigned to the positive and…
We propose a novel calibration method for computer simulators, dealing with the problem of covariate shift. Covariate shift is the situation where input distributions for training and test are different, and ubiquitous in applications of…
This paper deals with the error analysis of the trapezoidal rule for the computation of Fourier type integrals, based on two double exponential transformations. The theory allows to construct algorithms in which the steplength and the…
Spread options are a fundamental class of derivative contract written on multiple assets, and are widely used in a range of financial markets. There is a long history of approximation methods for computing such products, but as yet there is…
Building on techniques developed by Lyons and Victoir, we present the first explicit construction of a degree-7 cubature formula for Wiener space over $\mathbb{R}^3$. We then examine and compare two approaches for computing cubature…
A procedure is suggested for testing the resolution and comparing the relative accuracy of numerical schemes for integration of the incompressible Euler equations.
Quasi-Monte Carlo cubature methods often sample the integrand using Sobol' (or other digital) sequences to obtain higher accuracy than IID sampling. An important question is how to conservatively estimate the error of a digital sequence…
In Bayesian inference for mixture models with an unknown number of components, a finite mixture model is usually employed that assumes prior distributions for mixing weights and the number of components. This model is called a mixture of…
For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…
We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, so that the…
Utilising classical results on the structure of Hopf algebras, we develop a novel approach for the construction of cubature formulae on Wiener space based on unshuffle expansions. We demonstrate the effectiveness of this approach by…
Inverse medium scattering problems arise in many applications, but in practice, the measurement data are often restricted to a limited aperture by physical or experimental constraints. Classical sampling methods, such as MUSIC and the…
This paper introduces a weighted generalized inverse framework for Fourier extensions, designed to suppress spurious oscillations in the extended region while maintaining high approximation accuracy on the original interval. By formulating…
This paper presents a new finite difference algorithm for solving the 2D one-way wave equation with a preliminary approximation of a pseudo-differential operator by a system of partial differential equations. As opposed to the existing…