Asymptotically tight worst case complexity bounds for initial-value problems with nonadaptive information

TL;DR

This paper establishes asymptotically tight worst-case complexity bounds for solving initial-value problems using nonadaptive information, closing a significant gap in understanding the efficiency limits of such algorithms.

Contribution

It provides the first asymptotically matching lower and upper bounds for nonadaptive information in initial-value problems, including a broader class of nonadaptive linear information.

Findings

Established asymptotically tight complexity bounds for nonadaptive algorithms.

Demonstrated that bounds depend on the number of equations.

Extended results to a general class of nonadaptive linear information.

Abstract

It is known that, for systems of initial-value problems, algorithms using adaptive information perform much better in the worst case setting than the algorithms using nonadaptive information. In the latter case, lower and upper complexity bounds significantly depend on the number of equations. However, in contrast with adaptive information, existing lower and upper complexity bounds for nonadaptive information are not asymptotically tight. In this paper, we close the gap in the complexity exponents, showing asymptotically matching bounds for nonadaptive standard information, as well as for a more general class of nonadaptive linear information.