Pith. sign in

REVIEW 1 cited by

Bounds on Kolmogorov widths and sampling recovery for classes with small mixed smoothness

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2012.09925 v1 pith:XMDNSN3D submitted 2020-12-17 math.NA cs.NAmath.FA

V. Temlyakov , T. Ullrich This is my paper · ORCID
classification math.NAcs.NAmath.FA
keywords mixedsmoothnessboundsclasseskolmogorovsmallwidthsfunctions
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
abstract

Results on asymptotic characteristics of classes of functions with mixed smoothness are obtained in the paper. Our main interest is in estimating the Kolmogorov widths of classes with small mixed smoothness. We prove the corresponding bounds for the unit balls of the trigonometric polynomials with frequencies from a hyperbolic cross. We demonstrate how our results on the Kolmogorov widths imply new upper bounds for the optimal sampling recovery in the $L_2$ norm of functions with small mixed smoothness.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Some lower bounds for optimal sampling recovery of functions with mixed smoothness

    math.NA 2024-12 conditional novelty 6.0 of 10

    Optimal nonlinear sampling recovery of mixed-smoothness classes H^r_q is at least c m^{-r+1/q-1/p} (log m)^{(d-1)/p}, a logarithmic factor not captured by previous lower-bound techniques.

Pith tools