Related papers: New results on quasi-subfield polynomials
We introduce the Shifted Legendre Symbol Problem and some variants along with efficient quantum algorithms to solve them. The problems and their algorithms are different from previous work on quantum computation in that they do not appear…
Quasipolynomial (or QP) mappings constitute a wide generalization of the well-known Lotka-Volterra mappings, of importance in different fields such as population dynamics, Physics, Chemistry or Economy. In addition, QP mappings are a…
An important problem in applications of quasiconformal analysis and in its numerical aspect is to establish algorithms for explicit or approximate determination of the basic quasiinvariant curvelinear and analytic functionals intrinsically…
In the present paper we study the existence of solutions for some classes of singular systems involving the p(x) and q(x) Laplacian operators. The approach is based on bifurcation theory and subsupersolution method for systems of…
In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange…
In this note we examine the a priori and a posteriori analysis of discontinuous Galerkin finite element discretisations of semilinear elliptic PDEs with polynomial nonlinearity. We show that optimal a priori error bounds in the energy norm…
Purely multiplicative comparisons of quantum relative entropy are desirable but challenging to prove. We show such comparisons for relative entropies between comparable densities, including the relative entropy of a density with respect to…
We study a class of semilinear elliptic equations on spaces of tempered ultradistributions of Beurling and Roumieu type. Assuming that the linear part of the equation is an elliptic pseudodifferential operator of infinite order with a…
We introduce a novel semi-supervised version of the least squares classifier. This implicitly constrained least squares (ICLS) classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible…
We present a quantum algorithm for solving the hidden subgroup problem in the general linear group over a finite field where the hidden subgroup is promised to be a conjugate of the group of the invertible lower triangular matrices. The…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…
It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). Recently, several deep learning-based approximation algorithms for attacking this problem…
There has been growing interest in high-order tensor methods for nonconvex optimization, with adaptive regularization, as they possess better/optimal worst-case evaluation complexity globally and faster convergence asymptotically. These…
Quasi-convex optimization acts a pivotal part in many fields including economics and finance; the subgradient method is an effective iterative algorithm for solving large-scale quasi-convex optimization problems. In this paper, we…
Two problems are addressed: reduction of an arbitrary degree non-special divisor to the equivalent divisor of the degree equal to genus of a curve, and addition of divisors of arbitrary degrees. The hyperelliptic case is considered as the…
We study the integer minimization of a quasiconvex polynomial with quasiconvex polynomial constraints. We propose a new algorithm that is an improvement upon the best known algorithm due to Heinz (Journal of Complexity, 2005). This…
Recent works have shown that quantum computers can polynomially speed up certain SAT-solving algorithms even when the number of available qubits is significantly smaller than the number of variables. Here we generalise this approach. We…
We present new convergence analyses for parallel subspace correction methods for unconstrained semicoercive and nearly semicoercive convex optimization problems, generalizing the theory of singular and nearly singular linear problems to a…
In this article, we study pseudo-differential equations involving semi-quasielliptic symbols over p-adics. We determine the function spaces where such equations have solutions. We introduce the space of infinitely pseudo-differentiable…
In this paper we take a quasi-Newton approach to nonlinear eigenvalue problems (NEPs) of the type $M(\lambda)v=0$, where $M:\mathbb{C}\rightarrow\mathbb{C}^{n\times n}$ is a holomorphic function. We investigate which types of approximations…