A Stieltjes Algorithm for Generating Multivariate Orthogonal Polynomials

DOI10.1137/22m1477131zbMath1515.65045arXiv2202.04843OpenAlexW4378978085MaRDI QIDQ6155902

Akil C. Narayan, Zexin Liu

Publication date: 7 June 2023

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.04843

zbMATH Keywords

Stieltjes proceduremultivariate orthogonal polynomialsrecurrence coefficient matrices

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Algorithms for approximation of functions (65D15) Orthogonal polynomials and functions in several variables expressible in terms of basic hypergeometric functions in one variable (33D50) Numerical aspects of recurrence relations (65Q30)

Cites Work

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• Recursive three-term recurrence relations for the Jacobi polynomials on a triangle
• The numerically stable reconstruction of Jacobi matrices from spectral data
• On some orthogonal polynomials of interest in theoretical chemistry
• Determinantal processes and independence
• Growth of balls of holomorphic sections and energy at equilibrium
• Modified moments and Gaussian quadratures
• Pluripotential numerics
• On the computation of recurrence coefficients for univariate orthogonal polynomials
• Polynomial chaos expansions for dependent random variables
• Three term recurrence for the evaluation of multivariate orthogonal polynomials
• Orthogonal polynomials in two variables
• An algorithm for Gaussian quadrature given modified moments
• Formal properties of orthogonal polynomials in two variables
• Determinantal Point Processes for Machine Learning
• Polynomial interpolation and approximation in C^d
• The Recursion Formulas for Orthogonal Polynomials innVariables
• Orthogonality and Recursion Formulas for Polynomials in n Variables
• Recurrence Formulas for Multivariate Orthogonal Polynomials
• Multivariate Orthogonal Polynomials and Operator Theory
• Procrustes Problems
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Optimal weighted least-squares methods
• Near-Optimal Sampling Strategies for Multivariate Function Approximation on General Domains
• Multivariate approximation of functions on irregular domains by weighted least-squares methods
• A Sparse Spectral Method on Triangles
• On Multivariate Orthogonal Polynomials
• Orthogonal Polynomials of Several Variables
• Fast algorithms using orthogonal polynomials