Back to Search
Start Over
Adaptive Generalized Eigenvector Estimating Algorithm for Hermitian Matrix Pencil
- Source :
- IEEE/CAA Journal of Automatica Sinica. 9:1967-1979
- Publication Year :
- 2022
- Publisher :
- Institute of Electrical and Electronics Engineers (IEEE), 2022.
-
Abstract
- Generalized eigenvector plays an essential role in the signal processing field. In this paper, we present a novel neural network learning algorithm for estimating the generalized eigenvector of a Hermitian matrix pencil. Differently from some traditional algorithms, which need to select the proper values of learning rates before using, the proposed algorithm does not need a learning rate and is very suitable for real applications. Through analyzing all of the equilibrium points, it is proven that if and only if the weight vector of the neural network is equal to the generalized eigenvector corresponding to the largest generalized eigenvalue of a Hermitian matrix pencil, the proposed algorithm reaches to convergence status. By using the deterministic discrete-time method, some convergence conditions, which can be satisfied with probability 1, are also obtained to guarantee its convergence. Simulation results show that the proposed algorithm has a fast convergence speed and good numerical stability. The real application demonstrates its effectiveness in tracking the optimal vector of beamforming.
- Subjects :
- Control and Optimization
Artificial neural network
Computer science
Hermitian matrix
Artificial Intelligence
Control and Systems Engineering
Generalized eigenvector
Convergence (routing)
Weight
Algorithm
Pencil (mathematics)
Eigenvalues and eigenvectors
Information Systems
Numerical stability
Subjects
Details
- ISSN :
- 23299274 and 23299266
- Volume :
- 9
- Database :
- OpenAIRE
- Journal :
- IEEE/CAA Journal of Automatica Sinica
- Accession number :
- edsair.doi...........d474319794e50f3dd86aec4d869ee4cf