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Truncation dimension for linear problems on multivariate function spaces
- Source :
- Numerical Algorithms. 80:661-685
- Publication Year :
- 2018
- Publisher :
- Springer Science and Business Media LLC, 2018.
-
Abstract
- The paper considers linear problems on weighted spaces of multivariate functions of many variables. The main questions addressed are: When is it possible to approximate the solution for the original function of very many variables by the solution for the same function; however with all but the first $k$ variables set to zero, so that the corresponding error is small? What is the truncation dimension, i.e., the smallest number $k=k(\varepsilon)$ such that the corresponding error is bounded by a given error demand $\varepsilon$? Surprisingly, $k(\varepsilon)$ could be very small even for weights with a modest speed of convergence to zero.
- Subjects :
- Function space
Truncation
Applied Mathematics
Numerical analysis
Zero (complex analysis)
Numerical Analysis (math.NA)
010103 numerical & computational mathematics
Function (mathematics)
01 natural sciences
010101 applied mathematics
Dimension (vector space)
Bounded function
Convergence (routing)
FOS: Mathematics
Applied mathematics
Mathematics - Numerical Analysis
0101 mathematics
65Y20, 65D30
Mathematics
Subjects
Details
- ISSN :
- 15729265 and 10171398
- Volume :
- 80
- Database :
- OpenAIRE
- Journal :
- Numerical Algorithms
- Accession number :
- edsair.doi.dedup.....b6a51ad89ec8eb18c468f86561775da6