Related papers: Fast, Accurate Numerical Evaluation of Incomplete …
The status of numerical evaluations of Mellin-Barnes integrals is discussed, in particular, the application of the quasi-Monte Carlo integration package QMC to the efficient calculation of multi-dimensional integrals.
A key issue in the solution of partial differential equations via integral equation methods is the evaluation of possibly singular integrals involving the Green's function and its derivatives multiplied by simple functions over discretized…
Estimation of the energy of quantum many-body systems is a paradigmatic task in various research fields. In particular, efficient energy estimation may be crucial in achieving a quantum advantage for a practically relevant problem. For…
The implementation of discontinuous functions occurs in many of today's state-of-the-art partial differential equation solvers. However, in finite element methods, this poses an inherent difficulty: efficient quadrature rules available when…
The core of this thesis is the path-integral formulation of quantum field theory and its ability to describe strongly-coupled quantum many-body systems of finite size. Collective behaviors can be efficiently described in such systems…
The calculation and manipulation of large multi-variable rational functions is a key bottleneck in multi-loop calculations. In these conference proceedings, based on my article [Chawdhry (2023) arXiv:2312.03672], I present a technique to…
A purely numerical method, Direct ComputationMethod is applied to evaluate Feynman integrals. This method is based on the combination of an efficient numerical integration and an efficient extrapolation. In addition, high-precision…
The Fokker-Planck equation describing the transport of energetic particles interacting with turbulence is difficult to solve analytically. Numerical solutions are of course possible but they are not always useful for applications. In the…
The ideas behind the concept of algebraic ("integration-by-parts") algorithms for multiloop calculations are reviewed. For any topology and mass pattern, a finite iterative algebraic procedure is proved to exist which transforms the…
A fast non-polynomial interpolation is proposed in this paper for functions with logarithmic singularities. It can be executed fast with the discrete cosine transform. Based on this interpolation, a new quadrature is proposed for a kind of…
This work demonstrates algorithms to accurately compute solutions to thermal radiation transport problems using a reduced floating-point precision implementation of the Implicit Monte Carlo method. Several techniques falling into the…
In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In…
Both the no-core shell model and the effective interaction hyperspherical harmonic approaches are applied to the calculation of different response functions to external electromagnetic probes, using the Lorentz integral transform method.…
This paper deals with robust regression and subspace estimation and more precisely with the problem of minimizing a saturated loss function. In particular, we focus on computational complexity issues and show that an exact algorithm with…
We study a recently-proposed approach to the numerical evaluation of multi-loop Feynman integrals using available sector decomposition programs. As our main example, we consider the two-loop integrals for the $\alpha \alpha_s$ corrections…
Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector…
Invariant manifolds of unstable periodic orbits organize the dynamics of chaotic orbits in phase space. They provide insight into the mechanisms of transport and chaotic advection and have important applications in physical situations…
I present an algorithm for the reconstruction of multivariate rational functions from black-box probes. The arguably most important application in high-energy physics is the calculation of multi-loop and multi-leg amplitudes, where rational…
We discuss an integral equation approach that enables fast computation of the response of nonlinear multi-degree-of-freedom mechanical systems under periodic and quasi-periodic external excitation. The kernel of this integral equation is a…
We present an algorithm for the efficient numerical evaluation of integrals of the form \[ I(\omega) = \int_0^1 F( x,\mathrm e^{\mathrm i \omega x}; \omega) \, \mathrm d x \] for sufficiently smooth but otherwise arbitrary $F$ and $\omega…