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Concept

Classical orthogonal polynomials

Related publications (21)

Filter-Informed Spectral Graph Wavelet Networks for Multiscale Feature Extraction and Intelligent Fault Diagnosis

Olga Fink

Intelligent fault diagnosis has been increasingly improved with the evolution of deep learning (DL) approaches. Recently, the emerging graph neural networks (GNNs) have also been introduced in the field of fault diagnosis with the goal to make better use o ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

Numerical Studies of Brillouin-induced Polarization Pulling of Probe and Pump in Weakly-Birefringent Optical fibers with Applications to BOTDA

Luc Thévenaz, Marcelo Alfonso Soto Hernandez

Numerical solution of the involved governing equations confirm that the commonly used two orthogonal sets of gain- and loss-probes in BOTDA, differently affect the evolution of the pump state-of- polarization, thereby potentially compromising the minimizat ...

Optica Publishing Group2022

Finding a vocation for validation: taking proteomics beyond association and location

Yimon Aye, Jinmin Liu

First established in the seventies, proteomics, chemoproteomics, and most recently, spatial/proximity-proteomics technologies have empowered researchers with new capabilities to illuminate cellular communication networks that govern sophisticated decision- ...

ROYAL SOC CHEMISTRY2022

Hidden-nucleons neural-network quantum states for the nuclear many-body problem

Giuseppe Carleo

We generalize the hidden-fermion family of neural network quantum states to encompass both continuous and discrete degrees of freedom and solve the nuclear many-body Schrodinger equation in a systematically improvable fashion. We demonstrate that adding hi ...

AMER PHYSICAL SOC2022

Strictly Real Fundamental Theorem Of Algebra Using Polynomial Interlacing

Soham Basu

Without resorting to complex numbers or any advanced topological arguments, we show that any real polynomial of degree greater than two always has a real quadratic polynomial factor, which is equivalent to the fundamental theorem of algebra. The proof uses ...

CAMBRIDGE UNIV PRESS2021

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from anisotropic clustering analysis of the quasar sample in configuration space between redshift 0.8 and 2.2

Cheng Zhao

We measure the anisotropic clustering of the quasar sample from Data Release 16 (DR16) of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey (eBOSS). A sample of 343 708 spectroscopically confirmed quasars between redshift 0.8 ...

OXFORD UNIV PRESS2021

Computation of Al-Salam Carlitz and Askey-Wilson moments using Motzkin paths

Gaspard Ohlmann

In this paper we study the moments of polynomials from the Askey scheme, and we focus on Askey-Wilson polynomials. More precisely, we give a combinatorial proof for the case where d = 0. Their values have already been computed by Kim and Stanton in 2015, h ...

ELECTRONIC JOURNAL OF COMBINATORICS2021

A p-weighted limiter for the discontinuous Galerkin method on one-dimensional and two-dimensional triangular grids

Qian Wang, Qian Wang

This paper presents an accuracy-preserving p-weighted limiter for discontinuous Galerkin methods on one-dimensional and two-dimensional triangular grids. The p-weighted limiter is the extension of the second-order WENO limiter by Li et al. [W. Li, J. Pan a ...

2020

Asian option pricing with orthogonal polynomials

Sander Félix M Willems

In this paper we derive a series expansion for the price of a continuously sampled arithmetic Asian option in the Black-Scholes setting. The expansion is based on polynomials that are orthogonal with respect to the log-normal distribution. All terms in the ...

ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD2019

Option pricing with orthogonal polynomial expansions

Damir Filipovic, Damien Edouard Ackerer

We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that our polynomial ...

2020

A New Approach For American Option Pricing: The Dynamic Chebyshev Method

Kathrin Beatrice Glau

We introduce a new method to price American options based on Chebyshev interpolation. In each step of a dynamic programming time-stepping we approximate the value function with Chebyshev polynomials. The key advantage of this approach is that it allows us ...

2019

Distributed Signal Processing via Chebyshev Polynomial Approximation

Pascal Frossard, Pierre Vandergheynst, Daniel Kressner, David Shuman

Unions of graph multiplier operators are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators. The proposed method features approximations of ...

2018

New Algorithmic Paradigms for Discrete Problems using Dynamical Systems and Polynomials

Damian Mateusz Straszak

Optimization is a fundamental tool in modern science. Numerous important tasks in biology, economy, physics and computer science can be cast as optimization problems. Consider the example of machine learning: recent advances have shown that even the most s ...

EPFL2018

Conic Programming Reformulations of Two-Stage Distributionally Robust Linear Programs over Wasserstein Balls

Daniel Kuhn, Grani Adiwena Hanasusanto

Adaptive robust optimization problems are usually solved approximately by restricting the adaptive decisions to simple parametric decision rules. However, the corresponding approximation error can be substantial. In this paper we show that two-stage robust ...

2018

Momentum-space conformal blocks on the light cone

Marc Gillioz

We study the momentum-space 4-point correlation function of identical scalar operators in conformal field theory. Working specifically with null momenta, we show that its imaginary part admits an expansion in conformal blocks. The blocks are polynomials in ...

Springer Nature2018

Verification and validation procedures with applications to plasma-edge turbulence simulations

Fabio Riva

Understanding the plasma dynamics in tokamaks is of fundamental importance to reliably predict the performances of future fusion devices. Because of the complex phenomena at play, state-of-the-art simulation codes are needed to investigate the plasma dynam ...

EPFL2017

Uncertainty propagation by using spectral methods: A practical application to a two-dimensional turbulence fluid model

Paolo Ricci, Fabio Riva

To reduce the computational cost of the uncertainty propagation analysis, which is used to study the impact of input parameter variations on the results of a simulation, a general and simple to apply methodology based on decomposing the solution to the mod ...

American Institute of Physics2017

Generalized Gauss Inequalities via Semidefinite Programming

Daniel Kuhn

A sharp upper bound on the probability of a random vector falling outside a polytope, based solely on the first and second moments of its distribution, can be computed efficiently using semidefinite programming. However, this Chebyshev-type bound tends to ...

Springer Verlag2016

A Bi-Criteria Approximation Algorithm for k-Means

Justin Dean Ward

We consider the classical k-means clustering problem in the setting of bi-criteria approximation, in which an algorithm is allowed to output beta*k > k clusters, and must produce a clustering with cost at most alpha times the to the cost of the optimal set ...

Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik2016

A Multi-domain Spectral Method for Time-fractional Differential Equations

Jan Sickmann Hesthaven

This paper proposes an approach for high-order time integration within a multi-domain setting for time- fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to p ...

Elsevier2015