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 41 articles , 1 standard article )

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  1. 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)
  2. 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)
  3. Bourquin, Raoul: Algorithms for the construction of high-order Kronrod rule extensions with application to sparse-grid integration (2017)
  4. 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)
  5. Barajas-Solano, David A.; Tartakovsky, Daniel M.: Stochastic collocation methods for nonlinear parabolic equations with random coefficients (2016)
  6. Ko, Jordan; Wynn, Henry P.: The algebraic method in quadrature for uncertainty quantification (2016)
  7. 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)
  8. Nobile, Fabio; Tamellini, Lorenzo; Tesei, Francesco; Tempone, Raúl: An adaptive sparse grid algorithm for elliptic PDEs with lognormal diffusion coefficient (2016)
  9. Rahman, Sharif; Ren, Xuchun; Yadav, Vaibhav: High-dimensional stochastic design optimization by adaptive-sparse polynomial dimensional decomposition (2016)
  10. Chen, Michael; Mehrotra, Sanjay; Papp, Dávid: Scenario generation for stochastic optimization problems via the sparse grid method (2015)
  11. Constantine, Paul G.: Active subspaces. Emerging ideas for dimension reduction in parameter studies (2015)
  12. Lei, H.; Yang, X.; Zheng, B.; Lin, G.; Baker, N.A.: Constructing surrogate models of complex systems with enhanced sparsity: quantifying the influence of conformational uncertainty in biomolecular solvation (2015)
  13. Zhang, Zhongqiang; Tretyakov, Michael V.; Rozovskii, Boris; Karniadakis, George E.: Wiener chaos versus stochastic collocation methods for linear advection-diffusion-reaction equations with multiplicative white noise (2015)
  14. Beck, Joakim; Nobile, Fabio; Tamellini, Lorenzo; Tempone, Raúl: A quasi-optimal sparse grids procedure for groundwater flows (2014)
  15. Da Fonseca, José; Grasselli, Martino; Ielpo, Florian: Estimating the Wishart affine stochastic correlation model using the empirical characteristic function (2014)
  16. Geraci, Marco; Bottai, Matteo: Linear quantile mixed models (2014)
  17. Horwood, Joshua T.; Poore, Aubrey B.: Gauss von Mises distribution for improved uncertainty realism in space situational awareness (2014)
  18. Narayan, Akil; Jakeman, John D.: Adaptive Leja sparse grid constructions for stochastic collocation and high-dimensional approximation (2014)
  19. Yadav, Vaibhav; Rahman, Sharif: Adaptive-sparse polynomial dimensional decomposition methods for high-dimensional stochastic computing (2014)
  20. Zhang, Xin-Chun; Teng, Yun-Long: A new derivation of the cubature Kalman filters (2014)

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