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Lazy evaluation in infinite-dimensional function spaces with wavelet basis
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.). Faculty of Engineering and Science, Western Norway University of Applied Science, Bergen, Norway.
2019 (English)In: FHPNC 2019 - Proceedings of the 8th ACM SIGPLAN International Workshop on Functional High-Performance and Numerical Computing, co-located with ICFP 2019, Association for Computing Machinery (ACM), 2019, p. 27-33Conference paper, Published paper (Refereed)
Abstract [en]

Vectors in numerical computation, i.e., arrays of numbers, often represent continuous functions. We would like to reflect this with types. One apparent obstacle is that spaces of functions are typically infinite-dimensional, while the code must run in finite time and memory. We argue that this can be overcome: even in an infinite-dimensional space, the vectors can in practice be stored in finite memory. However, dual vectors (corresponding essentially to distributions) require infinite data structure. The distinction is usually lost in the finite dimensional case, since dual vectors are often simply represented as vectors (by implicitly choosing a scalar product establishing the correspondence). However, we shall see that an explicit type-level distinction between functions and distributions makes sense and allows directly expressing useful concepts such as the Dirac distribution, which are problematic in the standard finite-resolution picture. The example implementation uses a very simple local basis that corresponds to a Haar Wavelet transform.

Place, publisher, year, edition, pages
Association for Computing Machinery (ACM), 2019. p. 27-33
Keywords [en]
Lazy evaluation, Multiresolution, Wavelet
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-262524DOI: 10.1145/3331553.3342615ISI: 000501489700003Scopus ID: 2-s2.0-85072534964ISBN: 9781450368148 (print)OAI: oai:DiVA.org:kth-262524DiVA, id: diva2:1362282
Conference
8th ACM SIGPLAN International Workshop on Functional High-Performance and Numerical Computing, FHPNC 2019, co-located with ICFP 2019, 18 August 2019, Berlin; Germany; 18 August 2019
Note

QC 20191018

Available from: 2019-10-18 Created: 2019-10-18 Last updated: 2020-01-07Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
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  • asciidoc
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