Revisiting time-variant complex conjugate matrix equations with their corresponding real field time-variant large-scale linear equations, neural hypercomplex numbers space compressive approximation approach

TL;DR

This paper introduces neural dynamic models for complex conjugate matrix equations, transforming them into real field equations, and proposes a hypercomplex approximation method, with experiments validating the models' effectiveness.

Contribution

It presents a novel neural hypercomplex numbers space compressive approximation approach and models for time-variant complex conjugate matrix equations, enhancing computational efficiency and accuracy.

Findings

Con-CZND1 model is more efficient due to fewer elements.

Transforming to real field affects performance based on matrix properties.

NHNSCAA improves approximation accuracy and computational performance.

Abstract

Large-scale linear equations and high dimension have been hot topics in deep learning, machine learning, control,and scientific computing. Because of special conjugate operation characteristics, time-variant complex conjugate matrix equations need to be transformed into corresponding real field time-variant large-scale linear equations. In this paper, zeroing neural dynamic models based on complex field error (called Con-CZND1) and based on real field error (called Con-CZND2) are proposed for in-depth analysis. Con-CZND1 has fewer elements because of the direct processing of complex matrices. Con-CZND2 needs to be transformed into the real field, with more elements, and its performance is affected by the main diagonal dominance of coefficient matrices. A neural hypercomplex numbers space compressive approximation approach (NHNSCAA) is innovatively proposed. Then Con-CZND1 conj model is constructed. Numerical experiments verify Con-CZND1 conj model effectiveness and highlight NHNSCAA importance.