Related papers: Computation of highly oscillatory Bessel transform…
This paper presents low-complexity tensor completion algorithms and their efficient implementation to reconstruct highly oscillatory operators discretized as $n\times n$ matrices. The underlying tensor decomposition is based on the…
We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution…
We propose a new splitting method for strong numerical solution of the Cox-Ingersoll-Ross model. For this method, applied over both deterministic and adaptive random meshes, we prove a uniform moment bound and strong error results of order…
In this work we develop the Gaussian quadrature rule for weight functions involving fractional powers, exponentials and Bessel functions of the first kind. Besides the computation based on the use of the standard and the modified Chebyshev…
The Fourier Transform is one of the most important linear transformations used in science and engineering. Cooley and Tukey's Fast Fourier Transform (FFT) from 1964 is a method for computing this transformation in time $O(n\log n)$. From a…
We study relevant deformations of conformal field theory on a cylinder using conformal perturbation theory, and in particular the one point function of the deformation operator and the energy in a system after a quench. We do the one point…
Discrete analogs of the Lebedev-Skalskaya transforms are introduced and investigated. It involves series and integrals with respect to the kernels ${\rm Re} K_{\alpha+in}(x), {\rm Im} K_{\alpha+in}(x), x >0, n \in \mathbb{N}, |\alpha | <…
The bottleneck of micromagnetic simulations is the computation of the long-ranged magnetostatic fields. This can be tackled on regular N-node grids with Fast Fourier Transforms in time N logN, whereas the geometrically more versatile finite…
We present an efficient transcription method for highly oscillatory optimal control problems. For these problems, the optimal state trajectory consists of fast oscillations that change slowly over the time horizon. Out of a large number of…
Computation of moments of transformed random variables is a problem appearing in many engineering applications. The current methods for moment transformation are mostly based on the classical quadrature rules which cannot account for the…
A backward computation method has been developed to accelerate modelling of the critical state magnetization current in a staggered-array bulk high-temperature superconducting (HTS) undulator. The key concept is as follows: i) a large…
Let $X$ be a complete, simply connected harmonic manifold with sectional curvatures $K$ satisfying $K \leq -1$, and let $\partial X$ denote the boundary at infinity of $X$. Let $h > 0$ denote the mean curvature of horospheres in $X$, and…
This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and…
In this paper, an efficient modified Newton type algorithm is proposed for nonlinear unconstrianed optimization problems. The modified Hessian is a convex combination of the identity matrix (for steepest descent algorithm) and the Hessian…
We develop optimization methods which offer new trade-offs between the number of gradient and Hessian computations needed to compute the critical point of a non-convex function. We provide a method that for any twice-differentiable $f\colon…
A new, fast second-order method is proposed that achieves the optimal $\mathcal{O}\left(|\log(\epsilon)|\epsilon^{-3/2}\right)$ complexity to obtain first-order $\epsilon$-stationary points. Crucially, this is deduced without assuming the…
We introduce a framework for simulating hybrid oscillator-qubit quantum processors on qubit-only systems through position encoding. By encoding continuous-variable position and momentum wave functions into qubit amplitudes, our method…
In this paper, we present a numerical homogenization scheme for indefinite, time-harmonic Maxwell's equations involving potentially rough (rapidly oscillating) coefficients. The method involves an $\mathbf{H}(\mathrm{curl})$-stable,…
The paper presents a numerical analysis of the class of mathematical models of linear fractional oscillators, which is the Cauchy problem for a differential equation with derivatives of fractional orders in the sense of Gerasimov-Caputo. A…
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…