Published June 2013
| public
Journal Article
Multiple point evaluation on combined tensor product supports
- Creators
- Hiptmair, R.
- Phillips, G.
- Sinha, G.
Abstract
We consider the multiple point evaluation problem for an n-dimensional space of functions [ − 1,1[^d ↦ℝ spanned by d-variate basis functions that are the restrictions of simple (say linear) functions to tensor product domains. For arbitrary evaluation points this task is faced in the context of (semi-)Lagrangian schemes using adaptive sparse tensor approximation spaces for boundary value problems in moderately high dimensions. We devise a fast algorithm for performing m ≥ n point evaluations of a function in this space with computational cost O(mlog^d n). We resort to nested segment tree data structures built in a reprocessing stage with an asymptotic effort of O(nlog^(d −1) n).
Additional Information
© 2013 Springer Science+Business Media, LLC. Received: 20 November 2011. Accepted: 9 July 2012. Published online: 26 July 2012. The authors would like to thank the two anonymous referees for their valuable suggestions.Additional details
- Eprint ID
- 39211
- DOI
- 10.1007/s11075-012-9624-4
- Resolver ID
- CaltechAUTHORS:20130703-103944279
- Created
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2013-07-03Created from EPrint's datestamp field
- Updated
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2021-11-09Created from EPrint's last_modified field