HRMSYM: A Fortran subroutine for the numerical computation of a vector integrals over an infinite region with a Gaussian weight function. This is software for an implementation of rules described in the paper ”Fully Symmetric Interpolatory Rules for Multiple Integrals over Infinite Regions with Gaussian Weight”. Also included is software for Gauss-Hermite product rules for a maximum of fifty points in each variable.

References in zbMATH (referenced in 55 articles , 1 standard article )

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  1. Gordon, Grey: Efficient VAR discretization (2021)
  2. van den Bos, L. M. M.; Sanderse, B.: A geometrical interpretation of the addition of nodes to an interpolatory quadrature rule while preserving positive weights (2021)
  3. Keshavarzzadeh, Vahid; Kirby, Robert M.; Narayan, Akil: Generation of nested quadrature rules for generic weight functions via numerical optimization: application to sparse grids (2020)
  4. Ballreich, Dominik: Stable and efficient cubature rules by metaheuristic optimization with application to Kalman filtering (2019)
  5. Karvonen, Toni; Särkkä, Simo; Oates, Chris. J.: Symmetry exploits for Bayesian cubature methods (2019)
  6. van Zandt, James R.: Efficient cubature rules (2019)
  7. Bayer, Christian; Siebenmorgen, Markus; Tempone, Raul: Smoothing the payoff for efficient computation of basket option prices (2018)
  8. Chen, Peng: Sparse quadrature for high-dimensional integration with Gaussian measure (2018)
  9. Dong, Zhaonan; Georgoulis, Emmanuil H.; Levesley, Jeremy; Usta, Fuat: A multilevel sparse kernel-based stochastic collocation finite element method for elliptic problems with random coefficients (2018)
  10. Ernst, Oliver G.; Sprungk, Björn; Tamellini, Lorenzo: Convergence of sparse collocation for functions of countably many Gaussian random variables (with application to elliptic PDEs) (2018)
  11. Farcas, Ionut-Gabriel; Uekermann, Benjamin; Neckel, Tobias; Bungartz, Hans-Joachim: Nonintrusive uncertainty analysis of fluid-structure interaction with spatially adaptive sparse grids and polynomial chaos expansion (2018)
  12. Karvonen, Toni; Särkkä, Simo: Fully symmetric kernel quadrature (2018)
  13. Berrone, Stefano; Pieraccini, Sandra; Scialò, Stefano: Non-stationary transport phenomena in networks of fractures: effective simulations and stochastic analysis (2017)
  14. Bourquin, Raoul: Algorithms for the construction of high-order Kronrod rule extensions with application to sparse-grid integration (2017)
  15. Liao, Qinzhuo; Zhang, Dongxiao; Tchelepi, Hamdi: A two-stage adaptive stochastic collocation method on nested sparse grids for multiphase flow in randomly heterogeneous porous media (2017)
  16. Barajas-Solano, David A.; Tartakovsky, Daniel M.: Stochastic collocation methods for nonlinear parabolic equations with random coefficients (2016)
  17. Haji-Ali, Abdul-Lateef; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raúl: Multi-index stochastic collocation for random PDEs (2016)
  18. Ko, Jordan; Wynn, Henry P.: The algebraic method in quadrature for uncertainty quantification (2016)
  19. Król, Agnieszka; Ferrer, Loïc; Pignon, Jean-Pierre; Proust-Lima, Cécile; Ducreux, Michel; Bouché, Olivier; Michiels, Stefan; Rondeau, Virginie: Joint model for left-censored longitudinal data, recurrent events and terminal event: predictive abilities of tumor burden for cancer evolution with application to the FFCD 2000--05 trial (2016)
  20. Nobile, Fabio; Tamellini, Lorenzo; Tesei, Francesco; Tempone, Raúl: An adaptive sparse grid algorithm for elliptic PDEs with lognormal diffusion coefficient (2016)

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