Notes on tractability conditions for linear multivariate problems

2018/07/09 by Peter Kritzer, Henryk Woźniakowski, Kritzer, Peter +1
Computer Science · Mathematics · #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Matrix Theory and Algorithms #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1807.03055

openalex publication_date 2018/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study approximations of compact linear multivariate operators defined over Hilbert spaces. We provide necessary and sufficient conditions on various notions of tractability. These conditions are mainly given in terms of sums of certain functions depending on the singular values of the multivariate problem. They do not require the ordering of these singular values which in many cases is difficult to achieve.

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