Research Group Prof. Griebel

Publications of Dr. Alexander Hullmann:

[1] M. Griebel, A. Hullmann, and P. Oswald. Optimal scaling parameters for sparse grid discretizations. Numerical Linear Algebra with Applications, 22(1):76-100, 2015. Also available as INS Preprint No. 1314.
[ bib | DOI | http | .pdf 1 ]

[2] A. Hullmann. The ANOVA decomposition and generalized sparse grid methods for the high-dimensional backward Kolmogorov equation. Dissertation, Institut für Numerische Simulation, Universität Bonn, 2015.
[ bib | .pdf (link) ]

[3] M. Griebel and A. Hullmann. A sparse grid based generative topographic mapping for the dimensionality reduction of high-dimensional data. In H. Bock, X. Hoang, R. Rannacher, and J. Schlöder, editors, Modeling, Simulation and Optimization of Complex Processes - HPSC 2012, pages 51-62. Springer International Publishing, 2014. Also available as INS Preprint No. 1206.
[ bib | DOI | http | .pdf 1 ]

[4] M. Griebel and A. Hullmann. On a multilevel preconditioner and its condition numbers for the discretized Laplacian on full and sparse grids in higher dimensions. In Singular Phenomena and Scaling in Mathematical Models, pages 263-296. Springer International Publishing Switzerland, 2014. Also available as INS Preprint No. 1301.
[ bib | .pdf 1 ]

[5] M. Griebel and A. Hullmann. Dimensionality reduction of high-dimensional data with a nonlinear principal component aligned generative topographic mapping. SIAM Journal on Scientific Computing, 36(3):A1027-A1047, 2014. Also available as INS Preprint No. 1311.
[ bib | DOI | http | .pdf 1 ]

[6] M. Griebel and A. Hullmann. An efficient sparse grid Galerkin approach for the numerical valuation of basket options under Kou's jump-diffusion model. In Sparse grids and Applications, Lecture Notes in Computational Science and Engineering, pages 121-150. Springer, 2013. Also available as INS Preprint No. 1202.
[ bib | .pdf 1 ]

[7] A. Hullmann. Schnelle Varianten des Generative Topographic Mapping. Diplomarbeit, Institut für Numerische Simulation, Universität Bonn, Dec. 2009.
[ bib | .pdf 1 ]

[1]	M. Griebel, A. Hullmann, and P. Oswald. Optimal scaling parameters for sparse grid discretizations. Numerical Linear Algebra with Applications, 22(1):76-100, 2015. Also available as INS Preprint No. 1314. [ bib \| DOI \| http \| .pdf 1 ]
[2]	A. Hullmann. The ANOVA decomposition and generalized sparse grid methods for the high-dimensional backward Kolmogorov equation. Dissertation, Institut für Numerische Simulation, Universität Bonn, 2015. [ bib \| .pdf (link) ]
[3]	M. Griebel and A. Hullmann. A sparse grid based generative topographic mapping for the dimensionality reduction of high-dimensional data. In H. Bock, X. Hoang, R. Rannacher, and J. Schlöder, editors, Modeling, Simulation and Optimization of Complex Processes - HPSC 2012, pages 51-62. Springer International Publishing, 2014. Also available as INS Preprint No. 1206. [ bib \| DOI \| http \| .pdf 1 ]
[4]	M. Griebel and A. Hullmann. On a multilevel preconditioner and its condition numbers for the discretized Laplacian on full and sparse grids in higher dimensions. In Singular Phenomena and Scaling in Mathematical Models, pages 263-296. Springer International Publishing Switzerland, 2014. Also available as INS Preprint No. 1301. [ bib \| .pdf 1 ]
[5]	M. Griebel and A. Hullmann. Dimensionality reduction of high-dimensional data with a nonlinear principal component aligned generative topographic mapping. SIAM Journal on Scientific Computing, 36(3):A1027-A1047, 2014. Also available as INS Preprint No. 1311. [ bib \| DOI \| http \| .pdf 1 ]
[6]	M. Griebel and A. Hullmann. An efficient sparse grid Galerkin approach for the numerical valuation of basket options under Kou's jump-diffusion model. In Sparse grids and Applications, Lecture Notes in Computational Science and Engineering, pages 121-150. Springer, 2013. Also available as INS Preprint No. 1202. [ bib \| .pdf 1 ]
[7]	A. Hullmann. Schnelle Varianten des Generative Topographic Mapping. Diplomarbeit, Institut für Numerische Simulation, Universität Bonn, Dec. 2009. [ bib \| .pdf 1 ]