相关论文: On numerical stability of recursive present value …
VQE is currently one of the most widely used algorithms for optimizing problems using quantum computers. A necessary step in this algorithm is calculating the expectation value given a state, which is calculated by decomposing the…
Conventional tomographic techniques are becoming increasingly infeasible for reconstructing the operators of quantum devices of growing sophistication. We describe a novel tomographic procedure using coherent states which begins by…
For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…
Near term quantum computers suffer from the presence of different noise sources. In order to mitigate for this effect and acquire results with significantly better accuracy, there is the urge of designing efficient error correction or error…
The underlying stochastic nature of the requirements for the Solvency II regulations has introduced significant challenges if the required calculations are to be performed correctly, without resorting to excessive approximations, within…
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From the construction of the algorithm, it is immediately…
In recent years, half precision floating-point arithmetic has gained wide support in hardware and software stack thanks to the advance of artificial intelligence and machine learning applications. Operating at half precision can…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the trajectory equation is obtained, and a few first order accurate…
The paper is concerned with a posteriori error bounds for a wide class of numerical schemes, for $n\times n$ hyperbolic conservation laws in one space dimension. These estimates are achieved by a "post-processing algorithm", checking that…
We propose a numerical recipe for risk evaluation defined by a backward stochastic differential equation. Using dual representation of the risk measure, we convert the risk valuation to a stochastic control problem where the control is a…
In this paper, a multivariate constrained robust M-regression (MCRM) method is developed to estimate shaping coefficients for electricity forward prices. An important benefit of the new method is that model arbitrage can be ruled out at an…
The problem of object restoration in the case of spatially incoherent illumination is considered. A regularized solution to the inverse problem is obtained through a probabilistic approach, and a numerical algorithm based on the statistical…
We study the stability with respect to perturbations and the accuracy of numerical algorithms for computing solutions to the multilinear PageRank problem $\mathbf{x} = (1-\alpha)\mathbf{v} + \alpha \mathcal{P} \mathbf{x}^2$. Our results…
We study two procedures (reverse-mode and forward-mode) for computing the gradient of the validation error with respect to the hyperparameters of any iterative learning algorithm such as stochastic gradient descent. These procedures mirror…
We present natural axisymmetric variants of schemes for curvature flows introduced earlier by the present authors and analyze them in detail. Although numerical methods for geometric flows have been used frequently in axisymmetric settings,…
We discuss how to evaluate the proximal operator of a convex and increasing function of a nuclear norm, which forms the key computational step in several first-order optimization algorithms such as (accelerated) proximal gradient descent…
In this paper, we present a probabilistic numerical algorithm combining dynamic programming, Monte Carlo simulations and local basis regressions to solve non-stationary optimal multiple switching problems in infinite horizon. We provide the…
The accuracy and stability of the Caltech-Cornell pseudospectral code is evaluated using the KST representation of the Einstein evolution equations. The basic "Mexico City Tests" widely adopted by the numerical relativity community are…
Scale-resolving simulations of high Reynolds number incompressible flows are often limited by the Courant-Friedrichs-Lewy (CFL) stability restriction imposed by explicit time-stepping schemes, resulting in small time step sizes and long…
This paper presents an analysis of the stochastic recursion $W_{i+1} = [V_iW_i+Y_i]^+$ that can be interpreted as an autoregressive process of order 1, reflected at 0. We start our exposition by a discussion of the model's stability…