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This is a header-only library providing a fast matrix-vector product and linear system solver for tensor product matrices with a downward-closed index set restriction. This can especially be applied to compute interpolation coefficients for a sparse grid basis or evaluate a sparse interpolant at sparse grid points. The library code is located in the src folder. This is a header-only library providing a fast matrix-vector product and linear system solver for tensor product matrices with a downward-closed index set restriction. This can especially be applied to compute interpolation coefficients for a sparse grid basis or evaluate a sparse interpolant at sparse grid points. The library code is located in the src folder.
The fast_sparse_interpolation library is published under an Apache 2.0 license. If you use this project for research purposes, please cite the following publication which describes the mathematical background: The fast_sparse_interpolation library is published under an Apache 2.0 license. If you use this project for research purposes, please cite the following publication which describes the mathematical background:
- David Holzmüller, Dirk Pflüger: Fast Sparse Grid Operations: A Unified Framework using Sparsified Generalized Triangular Tensor Products (currently submitted). - David Holzmüller, Dirk Pflüger: Fast Sparse Grid Operations using the Unidirectional Principle: A Generalized and Unified Framework (currently submitted).
The essential ideas behind the algorithm were first proposed in: The essential ideas behind the algorithm were first proposed in:
- Gustavo Avila and Tucker Carrington Jr.: A multi-dimensional Smolyak collocation method in curvilinear coordinates for computing vibrational spectra (2015). - Gustavo Avila and Tucker Carrington Jr.: A multi-dimensional Smolyak collocation method in curvilinear coordinates for computing vibrational spectra (2015).