Kazashi, Yoshihito; Suzuki, Yuya; Goda, Takashi Suboptimality of Gauss-Hermite quadrature and optimality of the trapezoidal rule for functions with finite smoothness. (English) Zbl 1516.65018 SIAM J. Numer. Anal. 61, No. 3, 1426-1448 (2023). MSC: 65D30 65D32 65Y20 33C45 PDFBibTeX XMLCite \textit{Y. Kazashi} et al., SIAM J. Numer. Anal. 61, No. 3, 1426--1448 (2023; Zbl 1516.65018) Full Text: DOI arXiv
Glau, Kathrin; Wunderlich, Linus The deep parametric PDE method and applications to option pricing. (English) Zbl 1510.91197 Appl. Math. Comput. 432, Article ID 127355, 21 p. (2022). MSC: 91G80 91G20 68T07 91G60 PDFBibTeX XMLCite \textit{K. Glau} and \textit{L. Wunderlich}, Appl. Math. Comput. 432, Article ID 127355, 21 p. (2022; Zbl 1510.91197) Full Text: DOI arXiv
Bartel, Felix; Potts, Daniel; Schmischke, Michael Grouped transformations and regularization in high-dimensional explainable ANOVA approximation. (English) Zbl 1515.62018 SIAM J. Sci. Comput. 44, No. 3, A1606-A1631 (2022). MSC: 62-08 62J10 PDFBibTeX XMLCite \textit{F. Bartel} et al., SIAM J. Sci. Comput. 44, No. 3, A1606--A1631 (2022; Zbl 1515.62018) Full Text: DOI arXiv
Feppon, Florian; Ammari, Habib Analysis of a Monte-Carlo Nystrom method. (English) Zbl 1507.65300 SIAM J. Numer. Anal. 60, No. 3, 1226-1250 (2022). MSC: 65R20 45A05 65C05 47B80 78M40 PDFBibTeX XMLCite \textit{F. Feppon} and \textit{H. Ammari}, SIAM J. Numer. Anal. 60, No. 3, 1226--1250 (2022; Zbl 1507.65300) Full Text: DOI
Rahman, Sharif; Jahanbin, Ramin A spline dimensional decomposition for uncertainty quantification in high dimensions. (English) Zbl 07524833 SIAM/ASA J. Uncertain. Quantif. 10, 404-438 (2022). MSC: 65-XX 49K30 60H35 65C60 PDFBibTeX XMLCite \textit{S. Rahman} and \textit{R. Jahanbin}, SIAM/ASA J. Uncertain. Quantif. 10, 404--438 (2022; Zbl 07524833) Full Text: DOI arXiv
Potts, D.; Schmischke, M. Learning multivariate functions with low-dimensional structures using polynomial bases. (English) Zbl 1476.65024 J. Comput. Appl. Math. 403, Article ID 113821, 19 p. (2022). MSC: 65D15 41A55 41A63 62J10 PDFBibTeX XMLCite \textit{D. Potts} and \textit{M. Schmischke}, J. Comput. Appl. Math. 403, Article ID 113821, 19 p. (2022; Zbl 1476.65024) Full Text: DOI arXiv
Griebel, Michael; Hamaekers, Jan Generalized sparse grid interpolation based on the fast discrete Fourier transform. (English) Zbl 1498.65039 Bungartz, Hans-Joachim (ed.) et al., Sparse grids and applications – Munich 2018. Selected papers based on the presentations at the fifth workshop, SGA2018, Munich, Germany, July 23–27, 2018. Cham: Springer. Lect. Notes Comput. Sci. Eng. 144, 53-68 (2021). MSC: 65D40 41A63 65D05 65T50 PDFBibTeX XMLCite \textit{M. Griebel} and \textit{J. Hamaekers}, Lect. Notes Comput. Sci. Eng. 144, 53--68 (2021; Zbl 1498.65039) Full Text: DOI
Leövey, H.; Römisch, W. Quasi-Monte Carlo methods for two-stage stochastic mixed-integer programs. (English) Zbl 1478.90068 Math. Program. 190, No. 1-2 (A), 361-392 (2021). MSC: 90C15 90C11 65C05 65D30 PDFBibTeX XMLCite \textit{H. Leövey} and \textit{W. Römisch}, Math. Program. 190, No. 1--2 (A), 361--392 (2021; Zbl 1478.90068) Full Text: DOI
Potts, Daniel; Schmischke, Michael Approximation of high-dimensional periodic functions with Fourier-based methods. (English) Zbl 1476.65022 SIAM J. Numer. Anal. 59, No. 5, 2393-2429 (2021). MSC: 65D15 42B05 41A55 41A63 62J10 65T40 65T50 PDFBibTeX XMLCite \textit{D. Potts} and \textit{M. Schmischke}, SIAM J. Numer. Anal. 59, No. 5, 2393--2429 (2021; Zbl 1476.65022) Full Text: DOI arXiv
Glau, Kathrin; Kressner, Daniel; Statti, Francesco Low-rank tensor approximation for Chebyshev interpolation in parametric option pricing. (English) Zbl 1452.91325 SIAM J. Financ. Math. 11, No. 3, 897-927 (2020). MSC: 91G60 65D05 91G20 PDFBibTeX XMLCite \textit{K. Glau} et al., SIAM J. Financ. Math. 11, No. 3, 897--927 (2020; Zbl 1452.91325) Full Text: DOI arXiv
Jahanbin, Ramin; Rahman, Sharif Stochastic isogeometric analysis in linear elasticity. (English) Zbl 1442.74253 Comput. Methods Appl. Mech. Eng. 364, Article ID 112928, 38 p. (2020). MSC: 74S70 74S60 65N30 65D07 65N75 74B05 74S22 PDFBibTeX XMLCite \textit{R. Jahanbin} and \textit{S. Rahman}, Comput. Methods Appl. Mech. Eng. 364, Article ID 112928, 38 p. (2020; Zbl 1442.74253) Full Text: DOI
Gnewuch, M.; Wnuk, M. Explicit error bounds for randomized Smolyak algorithms and an application to infinite-dimensional integration. (English) Zbl 1434.41028 J. Approx. Theory 251, Article ID 105342, 29 p. (2020). MSC: 41A63 60H25 68W20 PDFBibTeX XMLCite \textit{M. Gnewuch} and \textit{M. Wnuk}, J. Approx. Theory 251, Article ID 105342, 29 p. (2020; Zbl 1434.41028) Full Text: DOI arXiv
Rahman, Sharif Uncertainty quantification under dependent random variables by a generalized polynomial dimensional decomposition. (English) Zbl 1440.60044 Comput. Methods Appl. Mech. Eng. 344, 910-937 (2019). MSC: 60G99 62J10 60-08 PDFBibTeX XMLCite \textit{S. Rahman}, Comput. Methods Appl. Mech. Eng. 344, 910--937 (2019; Zbl 1440.60044) Full Text: DOI
Rahman, Sharif Dimensionwise multivariate orthogonal polynomials in general probability spaces. (English) Zbl 1433.42031 Appl. Math. Comput. 362, Article ID 124538, 19 p. (2019). MSC: 42C05 33C47 62J10 41A63 PDFBibTeX XMLCite \textit{S. Rahman}, Appl. Math. Comput. 362, Article ID 124538, 19 p. (2019; Zbl 1433.42031) Full Text: DOI arXiv
Xu, Xin; Luo, Xiaopeng; Rabitz, Herschel Numerical meshless solution of high-dimensional sine-Gordon equations via Fourier HDMR-HC approximation. (English) Zbl 1433.65245 J. Math. Chem. 57, No. 7, 1683-1699 (2019). MSC: 65M70 35Q53 65M06 PDFBibTeX XMLCite \textit{X. Xu} et al., J. Math. Chem. 57, No. 7, 1683--1699 (2019; Zbl 1433.65245) Full Text: DOI arXiv
Harase, Shin Comparison of Sobol’ sequences in financial applications. (English) Zbl 07061109 Monte Carlo Methods Appl. 25, No. 1, 61-74 (2019). MSC: 65C05 65D30 65C10 PDFBibTeX XMLCite \textit{S. Harase}, Monte Carlo Methods Appl. 25, No. 1, 61--74 (2019; Zbl 07061109) Full Text: DOI arXiv
Zhang, Jincheng; Fu, Song An efficient approach for quantifying parameter uncertainty in the SST turbulence model. (English) Zbl 1410.76140 Comput. Fluids 181, 173-187 (2019). MSC: 76K05 76F65 PDFBibTeX XMLCite \textit{J. Zhang} and \textit{S. Fu}, Comput. Fluids 181, 173--187 (2019; Zbl 1410.76140) Full Text: DOI
Jakeman, John D.; Narayan, Akil Generation and application of multivariate polynomial quadrature rules. (English) Zbl 1440.65036 Comput. Methods Appl. Mech. Eng. 338, 134-161 (2018). MSC: 65D32 65D30 PDFBibTeX XMLCite \textit{J. D. Jakeman} and \textit{A. Narayan}, Comput. Methods Appl. Mech. Eng. 338, 134--161 (2018; Zbl 1440.65036) Full Text: DOI arXiv
de Graaf, C. S. L.; Kandhai, D.; Reisinger, C. Efficient exposure computation by risk factor decomposition. (English) Zbl 1406.91489 Quant. Finance 18, No. 10, 1657-1678 (2018). MSC: 91G60 65C05 91G40 91G20 91G10 PDFBibTeX XMLCite \textit{C. S. L. de Graaf} et al., Quant. Finance 18, No. 10, 1657--1678 (2018; Zbl 1406.91489) Full Text: DOI arXiv
Chen, Peng Sparse quadrature for high-dimensional integration with Gaussian measure. (English) Zbl 06966736 ESAIM, Math. Model. Numer. Anal. 52, No. 2, 631-657 (2018). MSC: 65C20 65D30 65D32 65N12 65N15 65N21 PDFBibTeX XMLCite \textit{P. Chen}, ESAIM, Math. Model. Numer. Anal. 52, No. 2, 631--657 (2018; Zbl 06966736) Full Text: DOI arXiv
Zhang, Jincheng; Fu, Song An efficient Bayesian uncertainty quantification approach with application to \(k\)-\(\omega\)-\(\gamma\) transition modeling. (English) Zbl 1390.76121 Comput. Fluids 161, 211-224 (2018). MSC: 76F60 65C50 PDFBibTeX XMLCite \textit{J. Zhang} and \textit{S. Fu}, Comput. Fluids 161, 211--224 (2018; Zbl 1390.76121) Full Text: DOI
Dinh Dũng B-spline quasi-interpolation sampling representation and sampling recovery in Sobolev spaces of mixed smoothness. (English) Zbl 1382.41009 Acta Math. Vietnam. 43, No. 1, 83-110 (2018). MSC: 41A15 41A05 41A25 41A58 41A63 PDFBibTeX XMLCite \textit{Dinh Dũng}, Acta Math. Vietnam. 43, No. 1, 83--110 (2018; Zbl 1382.41009) Full Text: DOI arXiv
Luo, Xiaopeng; Xu, Xin; Rabitz, Herschel On the fundamental conjecture of HDMR: a Fourier analysis approach. (English) Zbl 1385.42002 J. Math. Chem. 55, No. 2, 632-660 (2017). MSC: 42A10 65D99 42A16 PDFBibTeX XMLCite \textit{X. Luo} et al., J. Math. Chem. 55, No. 2, 632--660 (2017; Zbl 1385.42002) Full Text: DOI
Weng, Chengfeng; Wang, Xiaoqun; He, Zhijian Efficient computation of option prices and Greeks by quasi-Monte Carlo method with smoothing and dimension reduction. (English) Zbl 1364.91152 SIAM J. Sci. Comput. 39, No. 2, B298-B322 (2017). MSC: 91G60 65C05 65D30 91G20 PDFBibTeX XMLCite \textit{C. Weng} et al., SIAM J. Sci. Comput. 39, No. 2, B298--B322 (2017; Zbl 1364.91152) Full Text: DOI
Dũng, Dinh Sampling and cubature on sparse grids based on a B-spline quasi-interpolation. (English) Zbl 1359.41001 Found. Comput. Math. 16, No. 5, 1193-1240 (2016). MSC: 41A15 41A05 41A25 41A58 41A63 PDFBibTeX XMLCite \textit{D. Dũng}, Found. Comput. Math. 16, No. 5, 1193--1240 (2016; Zbl 1359.41001) Full Text: DOI arXiv
Resmini, A.; Peter, J.; Lucor, D. Sparse grids-based stochastic approximations with applications to aerodynamics sensitivity analysis. (English) Zbl 1352.76093 Int. J. Numer. Methods Eng. 106, No. 1, 32-57 (2016). MSC: 76M25 65N75 76G25 PDFBibTeX XMLCite \textit{A. Resmini} et al., Int. J. Numer. Methods Eng. 106, No. 1, 32--57 (2016; Zbl 1352.76093) Full Text: DOI
Heitsch, H.; Leövey, H.; Römisch, W. Are quasi-Monte Carlo algorithms efficient for two-stage stochastic programs? (English) Zbl 1384.90067 Comput. Optim. Appl. 65, No. 3, 567-603 (2016). MSC: 90C15 PDFBibTeX XMLCite \textit{H. Heitsch} et al., Comput. Optim. Appl. 65, No. 3, 567--603 (2016; Zbl 1384.90067) Full Text: DOI arXiv
Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max; Burkardt, John Hyperspherical sparse approximation techniques for high-dimensional discontinuity detection. (English) Zbl 1386.65083 SIAM Rev. 58, No. 3, 517-551 (2016). MSC: 65D15 PDFBibTeX XMLCite \textit{G. Zhang} et al., SIAM Rev. 58, No. 3, 517--551 (2016; Zbl 1386.65083) Full Text: DOI
Franzelin, Fabian; Diehl, Patrick; Pflüger, Dirk Non-intrusive uncertainty quantification with sparse grids for multivariate peridynamic simulations. (English) Zbl 1343.74047 Griebel, Michael (ed.) et al., Meshfree methods for partial differential equations VII. Selected contributions based on the presentations at the 7th international workshop, Bonn, Germany, September 9–11, 2013. Cham: Springer (ISBN 978-3-319-06897-8/hbk; 978-3-319-06898-5/ebook). Lecture Notes in Computational Science and Engineering 100, 115-143 (2015). MSC: 74R99 74S30 PDFBibTeX XMLCite \textit{F. Franzelin} et al., Lect. Notes Comput. Sci. Eng. 100, 115--143 (2015; Zbl 1343.74047) Full Text: DOI
Peherstorfer, Benjamin; Gómez, Pablo; Bungartz, Hans-Joachim Reduced models for sparse grid discretizations of the multi-asset Black-Scholes equation. (English) Zbl 1336.91086 Adv. Comput. Math. 41, No. 5, 1365-1389 (2015). MSC: 91G60 65M60 65M22 35Q91 PDFBibTeX XMLCite \textit{B. Peherstorfer} et al., Adv. Comput. Math. 41, No. 5, 1365--1389 (2015; Zbl 1336.91086) Full Text: DOI Link
Peherstorfer, Benjamin; Zimmer, Stefan; Zenger, Christoph; Bungartz, Hans-Joachim A multigrid method for adaptive sparse grids. (English) Zbl 06502304 SIAM J. Sci. Comput. 37, No. 5, S51-S70 (2015). MSC: 65F10 65N22 65N55 PDFBibTeX XMLCite \textit{B. Peherstorfer} et al., SIAM J. Sci. Comput. 37, No. 5, S51--S70 (2015; Zbl 06502304) Full Text: DOI Link
Zhang, G.; Webster, C.; Gunzburger, M.; Burkardt, J. A hyperspherical adaptive sparse-grid method for high-dimensional discontinuity detection. (English) Zbl 1317.65058 SIAM J. Numer. Anal. 53, No. 3, 1508-1536 (2015). MSC: 65D15 PDFBibTeX XMLCite \textit{G. Zhang} et al., SIAM J. Numer. Anal. 53, No. 3, 1508--1536 (2015; Zbl 1317.65058) Full Text: DOI Link
Leövey, H.; Römisch, W. Quasi-Monte Carlo methods for linear two-stage stochastic programming problems. (English) Zbl 1328.90092 Math. Program. 151, No. 1 (B), 315-345 (2015). MSC: 90C15 65D30 11K16 11K45 PDFBibTeX XMLCite \textit{H. Leövey} and \textit{W. Römisch}, Math. Program. 151, No. 1 (B), 315--345 (2015; Zbl 1328.90092) Full Text: DOI
Griebel, Michael; Hamaekers, Jan Fast discrete Fourier transform on generalized sparse grids. (English) Zbl 1316.65119 Garcke, Jochen (ed.) et al., Sparse grids and applications – Munich 2012. Proceedings of the 2nd workshop, SGA 2012, Munich, Germany, July 2–6, 2012. Cham: Springer (ISBN 978-3-319-04536-8/hbk; 978-3-319-04537-5/ebook). Lecture Notes in Computational Science and Engineering 97, 75-107 (2014). MSC: 65T50 42A15 PDFBibTeX XMLCite \textit{M. Griebel} and \textit{J. Hamaekers}, Lect. Notes Comput. Sci. Eng. 97, 75--107 (2014; Zbl 1316.65119) Full Text: DOI
Jiang, Lijian; Moulton, J. David; Wei, Jia A hybrid HDMR for mixed multiscale finite element methods with application to flows in random porous media. (English) Zbl 1312.76028 Multiscale Model. Simul. 12, No. 1, 119-151 (2014). MSC: 76M10 76S05 65N30 65N15 65C20 PDFBibTeX XMLCite \textit{L. Jiang} et al., Multiscale Model. Simul. 12, No. 1, 119--151 (2014; Zbl 1312.76028) Full Text: DOI arXiv
Dick, Josef; Gnewuch, Michael Infinite-dimensional integration in weighted Hilbert spaces: anchored decompositions, optimal deterministic algorithms, and higher-order convergence. (English) Zbl 1312.65002 Found. Comput. Math. 14, No. 5, 1027-1077 (2014). Reviewer: T. C. Mohan (Chennai) MSC: 65C05 11K38 46E22 PDFBibTeX XMLCite \textit{J. Dick} and \textit{M. Gnewuch}, Found. Comput. Math. 14, No. 5, 1027--1077 (2014; Zbl 1312.65002) Full Text: DOI arXiv
Yadav, Vaibhav; Rahman, Sharif Adaptive-sparse polynomial dimensional decomposition methods for high-dimensional stochastic computing. (English) Zbl 1296.62115 Comput. Methods Appl. Mech. Eng. 274, 56-83 (2014). MSC: 62H05 65C30 62J10 PDFBibTeX XMLCite \textit{V. Yadav} and \textit{S. Rahman}, Comput. Methods Appl. Mech. Eng. 274, 56--83 (2014; Zbl 1296.62115) Full Text: DOI arXiv
Rahman, Sharif Approximation errors in truncated dimensional decompositions. (English) Zbl 1297.41015 Math. Comput. 83, No. 290, 2799-2819 (2014). Reviewer: H. P. Dikshit (Bhopal) MSC: 41A63 65C60 PDFBibTeX XMLCite \textit{S. Rahman}, Math. Comput. 83, No. 290, 2799--2819 (2014; Zbl 1297.41015) Full Text: DOI arXiv
Dick, Josef; Gnewuch, Michael Optimal randomized changing dimension algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition. (English) Zbl 1296.41025 J. Approx. Theory 184, 111-145 (2014). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 41A55 28A25 65C05 65D32 65Y20 68W40 PDFBibTeX XMLCite \textit{J. Dick} and \textit{M. Gnewuch}, J. Approx. Theory 184, 111--145 (2014; Zbl 1296.41025) Full Text: DOI arXiv
Fujii, Masaaki Momentum-space approach to asymptotic expansion for stochastic filtering. (English) Zbl 1281.62214 Ann. Inst. Stat. Math. 66, No. 1, 93-120 (2014). MSC: 62M20 65T50 PDFBibTeX XMLCite \textit{M. Fujii}, Ann. Inst. Stat. Math. 66, No. 1, 93--120 (2014; Zbl 1281.62214) Full Text: DOI arXiv
Hu, Chao; Youn, Byeng D.; Yoon, Heonjun An adaptive dimension decomposition and reselection method for reliability analysis. (English) Zbl 1274.62672 Struct. Multidiscip. Optim. 47, No. 3, 423-440 (2013). MSC: 62N05 60H35 PDFBibTeX XMLCite \textit{C. Hu} et al., Struct. Multidiscip. Optim. 47, No. 3, 423--440 (2013; Zbl 1274.62672) Full Text: DOI
Wang, Hongchun An efficient dimension-adaptive uncertainty propagation approach. (English) Zbl 1244.65013 Appl. Math. Comput. 218, No. 7, 3230-3237 (2011). MSC: 65C60 65C05 62D05 PDFBibTeX XMLCite \textit{H. Wang}, Appl. Math. Comput. 218, No. 7, 3230--3237 (2011; Zbl 1244.65013) Full Text: DOI
Jakeman, John D.; Archibald, Richard; Xiu, Dongbin Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids. (English) Zbl 1218.65010 J. Comput. Phys. 230, No. 10, 3977-3997 (2011). MSC: 65C30 60H15 60H35 35R60 PDFBibTeX XMLCite \textit{J. D. Jakeman} et al., J. Comput. Phys. 230, No. 10, 3977--3997 (2011; Zbl 1218.65010) Full Text: DOI
Zhang, Zhongqiang; Choi, Minseok; Karniadakis, George Em Anchor points matter in ANOVA decomposition. (English) Zbl 1217.65039 Hesthaven, Jan S. (ed.) et al., Spectral and high order methods for partial differential equations. Selected papers from the 8th ICOSAHOM ’09 conference, Trondheim, Norway, June 22–26, 2009. Berlin: Springer (ISBN 978-3-642-15336-5/hbk; 978-3-642-15337-2/ebook). Lecture Notes in Computational Science and Engineering 76, 347-355 (2011). MSC: 65D15 65C30 60H15 60H35 PDFBibTeX XMLCite \textit{Z. Zhang} et al., Lect. Notes Comput. Sci. Eng. 76, 347--355 (2011; Zbl 1217.65039) Full Text: DOI