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Fast computation in adaptive tree approximation

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Summary.

Adaptive methods of approximation arise in many settings including numerical methods for PDEs and image processing. They can usually be described by a tree which records the adaptive decisions. This paper is concerned with the fast computation of near optimal trees based on n adaptive decisions. The best tree based on n adaptive decisions could be found by examining all such possibilities. However, this is exponential in n and could be numerically prohibitive. The main result of this paper is to show that it is possible to find near optimal trees using computations linear in n.

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References

  1. Binev, P., Dahmen, W., DeVore, R.: Adaptive finite element methods with convergence rates. IGPM Report # 218, RWTH Aachen, June 2002

  2. Cohen, A., Dahmen, W., Daubechies, I., DeVore, R.: Tree approximation and optimal encoding. Appl. Comp. Harm. Anal. 11, 192–226 (2001)

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Authors and Affiliations

  1. Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA

    Peter Binev & Ronald DeVore

Authors
  1. Peter Binev
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  2. Ronald DeVore
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Corresponding author

Correspondence to Ronald DeVore.

Additional information

Mathematics Subject Classification (2000): 65Y20, 65N50, 41A63, 41A15, 68W40, 68W25

This work has been supported in part by the Office of Naval Research contracts 03-10051, (N00014-00-1-0470), the Army Research Office contract DAAD 19-02-1-0028, and the National Science Foundation grants DMS 9872890, DMS 0221642.

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Binev, P., DeVore, R. Fast computation in adaptive tree approximation. Numer. Math. 97, 193–217 (2004). https://doi.org/10.1007/s00211-003-0493-6

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  • DOI: https://doi.org/10.1007/s00211-003-0493-6

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