Accelerated Algorithm for Splitting a Vector into Two Vectors with Small Uniform Norm

B. S. Kashin^ab, I. V. Oseledets^c, A. Rudikov<sup>c

a</sup> Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
^b Lomonosov Moscow State University
^c Artificial Intelligence Research Institute, Moscow

Abstract: We propose a fast algorithm for splitting an arbitrary vector into a sum of two vectors of small uniform norm (with respect to two different bases, of which one is random). The efficiency of the algorithm is supported by numerical experiments.

Keywords: random subsystem of an orthogonal system. greedy algorithm.

UDC: 517.5

Received: 05.06.2025

DOI: 10.4213/mzm14760

 English version: Mathematical Notes, 2025, 118:3, 564–570

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