Related papers: A practical framework for infinite-dimensional lin…
The paper presents a priori error analysis of the shallow neural network approximation to the solution to the indefinite elliptic equation and and cutting-edge implementation of the Orthogonal Greedy Algorithm (OGA) tailored to overcome the…
We introduce Yao, an extensible, efficient open-source framework for quantum algorithm design. Yao features generic and differentiable programming of quantum circuits. It achieves state-of-the-art performance in simulating small to…
Recently the Master Constraint Programme for Loop Quantum Gravity (LQG) was proposed as a classically equivalent way to impose the infinite number of Wheeler -- DeWitt constraint equations in terms of a single Master Equation. While the…
We investigate approximation algorithms for several fundamental optimization problems on geometric packing. The geometric objects considered are very generic, namely $d$-dimensional convex fat objects. Our main contribution is a versatile…
We study the partially asymmetric exclusion process with open boundaries. We generalise the matrix approach previously used to solve the special case of total asymmetry and derive exact expressions for the partition sum and currents valid…
We present a globally convergent SQP-type method with the least constraint violation for nonlinear semidefinite programming. The proposed algorithm employs a two-phase strategy coupled with a line search technique. In the first phase, a…
Approximating partial differential equations for extensive industrial and scientific applications requires leveraging the power of modern high-performance computing. In large-scale parallel computations, the geometrical discretisation…
While quantum weight enumerators establish some of the best upper bounds on the minimum distance of quantum error-correcting codes, these bounds are not optimized to quantify the performance of quantum codes under the effect of arbitrary…
We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds…
In this paper, we consider a class of nonconvex and nonsmooth fractional programming problems, that involve the sum of a convex, possibly nonsmooth function composed with a linear operator and a differentiable, possibly nonconvex function…
This paper presents a pioneering approach to solving the linear quadratic regulation (LQR) and linear quadratic tracking (LQT) problems with constrained inputs using a novel off-policy continuous-time Q-learning framework. The proposed…
To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional…
We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…
A key assumption in the theory of nonlinear adaptive control is that the uncertainty of the system can be expressed in the linear span of a set of known basis functions. While this assumption leads to efficient algorithms, it limits…
Recently developed quantum algorithms address computational challenges in numerical analysis by performing linear algebra in Hilbert space. Such algorithms can produce a quantum state proportional to the solution of a $d$-dimensional system…
Solutions to many partial differential equations satisfy certain bounds or constraints. For example, the density and pressure are positive for equations of fluid dynamics, and in the relativistic case the fluid velocity is upper bounded by…
In this paper, we propose a new easily implementable method for solving a class of semi-infinite programs, where an approximate linear semidefinite program is constructed for the concerned semi-infinite program based on the duality theory…
Constrained combinatorial optimization with strict linear constraints underpins applications in drug discovery, power grids, logistics, and finance, yet remains computationally demanding for classical algorithms, especially at large scales.…
Mixed-integer convex quadratic programs with indicator variables (MIQP) encompass a wide range of applications, from statistical learning to energy, finance, and logistics. The outer approximation (OA) algorithm has been proven efficient in…
We give infinite triangularization and strict triangularization results for algebras of operators on infinite dimensional vector spaces. We introduce a class of algebras we call Ore-solvable algebras: these are similar to iterated Ore…