# Average case tractability of additive random fields with Korobov kernels

## TL;DR

This paper studies the average case complexity of approximating additive random fields with Korobov kernels, establishing polynomial tractability and conditions for strong polynomial tractability under different error criteria.

## Contribution

It provides the first comprehensive analysis of tractability for these fields, including necessary and sufficient conditions for strong polynomial tractability.

## Key findings

- Problem is always polynomially tractable under ABS and NOR
- Derived necessary and sufficient conditions for strong polynomial tractability
- Analyzed non-homogeneous cases with Korobov kernels

## Abstract

We investigate average case tractability of approximation of additive random fields with marginal random processes corresponding to the Korobov kernels for the non-homogeneous case. We use the absolute error criterion (ABS) or the normalized error criterion (NOR). We show that the problem is always polynomially tractable for ABS or NOR, and give sufficient and necessary conditions for strong polynomial tractability for ABS or NOR.