Related papers: QCD Evolution Equations: Numerical Algorithms from…
In this paper we introduce a randomized version of the backward Euler method, that is applicable to stiff ordinary differential equations and nonlinear evolution equations with time-irregular coefficients. In the finite-dimensional case, we…
Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…
We present a generalization of the $x$-space $\texttt{Candia}$ algorithm to next-to-next-to-next-to-leading order (N$^3$LO) accuracy in Quantum Chromodynamics (QCD) for solving the DGLAP evolution equations for unpolarized parton densities…
The neighbourhood of the largest eigenvalue $\lambda_{\rm max}$ in the Gaussian unitary ensemble (GUE) and Laguerre unitary ensemble (LUE) is referred to as the soft edge. It is known that there exists a particular centring and scaling such…
An approach which unifies the Double Logarithmic Approximation at small x and the leading order DGLAP evolution of fragmentation functions at large x is presented. This approach reproduces exactly the Modified Leading Logarithm…
This work develops a distributed optimization strategy with guaranteed exact convergence for a broad class of left-stochastic combination policies. The resulting exact diffusion strategy is shown in Part II to have a wider stability range…
Spectral methods based on integral transforms may be efficiently used to solve differential equations in some special cases. This paper considers a different approach in which algorithms are proposed to calculate integral Laguerre transform…
A fundamental question in random matrix theory is to quantify the optimal rate of convergence to universal laws. We take up this problem for the Laguerre $\beta$ ensemble, characterised by the Dyson parameter $\beta$, and the Laguerre…
High-dimensional numerical optimization presents a persistent challenge in computational science. This paper introduces Quasi-Adaptive Search with Asymptotic Reinitialization (QUASAR), an evolutionary algorithm to accelerate convergence in…
In this paper we propose a general strategy for rapidly computing sparse Legendre expansions. The resulting methods yield a new class of fast algorithms capable of approximating a given function $f:[-1,1] \rightarrow \mathbb{R}$ with a…
We evaluate Generalized Parton Distributions of the pion in two chiral quark models: the Spectral Quark Model and the Nambu-Jona-Lasinio model with a Pauli-Villars regularization. We proceed by the evaluation of double distributions through…
Left-invariant PDE-evolutions on the roto-translation group $SE(2)$ (and their resolvent equations) have been widely studied in the fields of cortical modeling and image analysis. They include hypo-elliptic diffusion (for contour…
This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…
The Continuous p-Dispersion Problem (CpDP) with boundary constraints asks for the placement of a fixed number of points in a compact subset of Euclidean space such that the minimum distance between any two points, as well as the points and…
Methods for the computation of classical Gaussian quadrature rules are described which are effective both for small and large degree. These methods are reliable because the iterative computation of the nodes has guaranteed convergence, and…
We illustrate the implementation of a method based on the use of recursion relations in (Bjorken) $x-$space for the solution of the evolution equations of QCD for all the leading twist distributions. The algorithm has the advantage of being…
We provide a quantum method for simulating Hamiltonian evolution with complexity polynomial in the logarithm of the inverse error. This is an exponential improvement over existing methods for Hamiltonian simulation. In addition, its scaling…
A reduced-order model algorithm, based on approximations of Lax pairs, is proposed to solve nonlinear evolution partial differential equations. Contrary to other reduced-order methods, like Proper Orthogonal Decomposition, the space where…
To find the least squares solution of a very large and inconsistent system of equations, one can employ the extended Kaczmarz algorithm. This method simultaneously removes the error term, such that a consistent system is asymptotically…
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…