Pfaffian Systems of A-Hypergeometric Systems II --- Holonomic Gradient Method

2015/05/12 by Katsuyoshi Ohara, Ohara, Katsuyoshi, Nobuki Takayama +1 · 1 citation
Computer Science · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Computer and information sciences #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.1505.02947

openalex publication_date 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We give two efficient methods to derive Pfaffian systems for A-hypergeometric systems for the application to the holonomic gradient method for statistics. We utilize the Hilbert driven Buchberger algorithm and Macaulay type matrices in the two methods.

Citations

• Contiguity relations of Lauricella's F_D revisited
• Pfaffian Systems of A-Hypergeometric Equations I: Bases of Twisted Cohomology Groups
• Algebraic algorithms for sampling from conditional distributions
• Some Formulae in Elimination

Cited by

• On Conservative Matrix Fields: Continuous Asymptotics and Arithmetic

Related

• Comparison of Numerical Solvers for Differential Equations for Holonomic Gradient Method in Statistics
• Zeilberger's Holonomic Ansatz for Pfaffians
• On the parametric behavior of A-hypergeometric series
• A-Hypergeometric Distributions and Newton Polytopes
• Pfaffian Systems of A-Hypergeometric Equations I: Bases of Twisted Cohomology Groups