Bibliography¶

Selected references on sparse grids and sparse grid interpolation.

[1] H.-J. Bungartz and M. Griebel. Sparse grids. Acta Numerica, 13:147–269, 2004.

[2] A. Klimke and B. Wohlmuth. Algorithm 847: spinterp: Piecewise multilinear hierarchical sparse grid interpolation in MATLAB. ACM Transactions on Mathematical Software, 31(4), 2005.

[3] A. Klimke. Uncertainty Modeling using Fuzzy Arithmetic and Sparse Grids. PhD Thesis, Universität Stuttgart, Shaker Verlag, Aachen, 2006.

[4] V. Barthelmann, E. Novak, and K. Ritter. High dimensional polynomial interpolation on sparse grids. Advances in Computational Mathematics, 12(4):273–288, 2000.

[5] H.-J. Bungartz. Finite Elements of Higher Order on Sparse Grids. Shaker Verlag, Aachen, 1998.

[6] A. Klimke. Efficient construction of hierarchical polynomial sparse grid interpolants using the fast discrete cosine transform. Technical Report IANS Preprint 2006/007, Universität Stuttgart, 2006.

[7] M. Hegland. Adaptive sparse grids. In K. Burrage and R. B. Sidje, editors, Proceedings of the 2001 International Conference on Computational Techniques and Applications, University of Queensland, volume 44 of ANZIAM Journal, pages C335–C353, 2003.

[8] T. Gerstner and M. Griebel. Dimension-adaptive tensor-product quadrature. Computing, 71(1):65–87, 2003.

[9] T. N. L. Patterson. The Optimum Addition of Points to Quadrature Formulae. Mathematics of Computation, 22(104):847–856+s21–s31, 1968.

[10] T. Gerstner and M. Griebel. Numerical Integration using Sparse Grids. Numerical Algorithms, 18(3–4):209–232, 1998.