相关论文: Exterior products of operators and superoptimal an…
We derive a new Chambers-type formula and prove sharper upper bounds on the measure of the spectrum of critical almost Mathieu operators with rational frequencies.
The problem of extracting a well conditioned submatrix from any rectangular matrix (with normalized columns) has been studied for some time in functional and harmonic analysis; see…
The purpose of this paper is twofold: firstly, we present a new type of relationship between inverse problems and nonlinear differential equations. Secondly, we introduce a new type of inverse spectral problem, posed as follows: for a…
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios…
One of the unexplored benefits of studying layer potentials on smooth, closed hypersurfaces of Euclidean space is the factorization of the Neumann-Poincar\'e operator into a product of two self-adjoint transforms. Resurrecting some…
In this work, we propose an extensive numerical study on approximating the absolute value function. The methods presented in this paper compute approximants in the form of rational functions and have been proposed relatively recently, e.g.,…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
We propose an approach to factorize the time-evolution operator of a quantum system through a (finite) sequence of elementary operations that are time-ordered. Our proposal borrows from previous approaches based on Lie algebra techniques…
In this work, we consider robust submodular maximization with matroid constraints. We give an efficient bi-criteria approximation algorithm that outputs a small family of feasible sets whose union has (nearly) optimal objective value. This…
A multivariate version of Rosenblum's Fejer-Riesz theorem on outer factorization of trigonometric polynomials with operator coefficients is considered. Due to a simplification of the proof of the single variable case, new necessary and…
We study the q-analogue of Euler-Maclaurin formula and by introducing a new q-operator we drive to this form. Moreover, approximation properties of q-Bernoulli polynomials is discussed. We estimate the suitable functions as a combination of…
We study solutions of the Yang-Baxter equation on a tensor product of an arbitrary finite-dimensional and an arbitrary infinite-dimensional representations of the rank one symmetry algebra. We consider the cases of the Lie algebra sl_2, the…
We show how rational function approximations to the logarithm, such as $\log z \approx (z^2 - 1)/(z^2 + 6z + 1)$, can be turned into fast algorithms for approximating the determinant of a very large matrix. We empirically demonstrate that…
In this paper we introduce and study the concept of optimal and surely optimal dual martingales in the context of dual valuation of Bermudan options, and outline the development of new algorithms in this context. We provide a…
We present an alternative formalism for calculating the maximally localized Wannier functions in crystalline solids, obtaining an expression which is extremely simple and general. In particular, our scheme is exactly invariant under…
We introduce some general tools to design exact splitting methods to compute numerically semigroups generated by inhomogeneous quadratic differential operators. More precisely, we factorize these semigroups as products of semigroups that…
In this paper, we give direct theorems on point wise and global approximation by new variants of Bernstein-Durrmeyer operator, introduced by A.-M. et al.[1].
The method of choice to study one-dimensional strongly interacting many body quantum systems is based on matrix product states and operators. Such method allows to explore the most relevant, and numerically manageable, portion of an…
We describe two quantum algorithms to approximate the mean value of a black-box function. The first algorithm is novel and asymptotically optimal while the second is a variation on an earlier algorithm due to Aharonov. Both algorithms have…
It is known that multiplication of linear differential operators over ground fields of characteristic zero can be reduced to a constant number of matrix products. We give a new algorithm by evaluation and interpolation which is faster than…