Abstract
We consider approximation problems for a special space of d variate functions. We show that the problems have small number of active variables, as it has been postulated in the past using concentration of measure arguments. We also show that, depending on the norm for measuring the error, the problems are strongly polynomially or quasi-polynomially tractable even in the model of computation where functional evaluations have the cost exponential in the number of active variables.
Original language | English |
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Pages (from-to) | 76-91 |
Number of pages | 16 |
Journal | Journal of Complexity |
Volume | 29 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2013 |
Keywords
- Multivariate approximation
- Tractability
ASJC Scopus subject areas
- Algebra and Number Theory
- Statistics and Probability
- Numerical Analysis
- General Mathematics
- Control and Optimization
- Applied Mathematics