Related papers: Chebyshev Interpolation for Parametric Option Pric…
We develop a simple two-step algorithm for enclosing Chebyshev expansions whose cost is linear in terms of the polynomial degree. The algorithm first transforms the expansion from Chebyshev to the Laurent basis and then applies the interval…
The personalized PageRank algorithm is one of the most versatile tools for the analysis of networks. In spite of its ubiquity, maintaining personalized PageRank vectors when the underlying network constantly evolves is still a challenging…
Selection among alternative theoretical models given an observed data set is an important challenge in many areas of physics and astronomy. Reversible-jump Markov chain Monte Carlo (RJMCMC) is an extremely powerful technique for performing…
A new algebraic cubature formula of degree $2n+1$ for the product Chebyshev measure in the $d$-cube with $\approx n^d/2^{d-1}$ nodes is established. The new formula is then applied to polynomial hyperinterpolation of degree $n$ in three…
Global sensitivity analysis is employed to evaluate the effective dimension reduction achieved through Chebyshev interpolation and the conditional pathwise method for Greek estimation of discretely monitored barrier options and arithmetic…
Multiproposal MCMC (MP-MCMC) algorithms use clouds of proposals to efficiently traverse state spaces and overcome complex target geometries. While MCMC methods are embarrassingly parallel by nature, the non-trivial forms of parallelism…
Markov Decision Problems (MDPs) provide a foundational framework for modelling sequential decision-making across diverse domains, guided by optimality criteria such as discounted and average rewards. However, these criteria have inherent…
We propose an algorithm for generating explicit solutions of multiparametric mixed-integer convex programs to within a given suboptimality tolerance. The algorithm is applicable to a very general class of optimization problems, but is most…
We introduce a computational method to discover polymorphs in molecular crystals at finite temperature. The method is based on reproducing the crystallization process starting from the liquid and letting the system discover the relevant…
Asynchronous iterations arise naturally in parallel computing if one wants to solve large problems with a minimization of the idle times. This paper presents an original model of asynchronous iterations for a time-domain decomposition…
This article presents a high-order accurate numerical method for the evaluation of singular volume integral operators, with attention focused on operators associated with the Poisson and Helmholtz equations in two dimensions. Following the…
Inspired by a series of remarkable papers in recent years that use Deep Neural Nets to substantially speed up the calibration of pricing models, we investigate the use of Chebyshev Tensors instead of Deep Neural Nets. Given that Chebyshev…
Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and…
We investigate the problem of numerical differentiation of bivariate functions from weighted Wiener classes using Chebyshev polynomial expansions. We develop and analyze a new version of the truncation method based on Chebyshev polynomials…
We describe a high performance parallel implementation of a derivative pricing model, within which we introduce a new parallel method for the calibration of the industry standard SABR (stochastic-\alpha \beta \rho) stochastic volatility…
Constrained decision-making is essential for designing safe policies in real-world control systems, yet simulated environments often fail to capture real-world adversities. We consider the problem of learning a policy that will maximize the…
The problem of optimizing over the cone of nonnegative polynomials is a fundamental problem in computational mathematics, with applications to polynomial optimization, control, machine learning, game theory, and combinatorics, among others.…
In recent decades, new methods and approaches have been developed for forecasting intermittent demand series. However, the majority of research has focused on point forecasting, with little exploration into probabilistic intermittent demand…
For the cascaded planning and control modules implemented for robot navigation, the frequency gap between the planner and controller has received limited attention. In this study, we introduce a novel B-spline parameterized…
The Numerical Recipes series of books are a useful resource, but all the algorithms they contain cannot be used within open-source projects. In this paper we develop drop-in alternatives to the two algorithms they present for cubic spline…