Generalized Polynomial Power Method
- Resource Type
- Conference
- Authors
- Khattak, Faizan A.; Proudler, Ian K.; Weiss, Stephan
- Source
- 2023 Sensor Signal Processing for Defence Conference (SSPD) Sensor Signal Processing for Defence Conference (SSPD), 2023. :1-5 Sep, 2023
- Subject
- Aerospace
Communication, Networking and Broadcast Technologies
Components, Circuits, Devices and Systems
Computing and Processing
Fields, Waves and Electromagnetics
Photonics and Electrooptics
Robotics and Control Systems
Signal Processing and Analysis
Signal processing algorithms
Estimation
Signal processing
Approximation algorithms
Eigenvalues and eigenfunctions
Matrix decomposition
- Language
The polynomial power method repeatedly multiplies a polynomial vector by a para-Hermitian matrix containing spectrally majorised eigenvalue to estimate the dominant eigenvector corresponding to the dominant eigenvalue. To limit the order of the resulting vector, truncation is performed in each iteration. This paper extends the polynomial power method from para-Hermitian matrices to a general polynomial matrix for determining its dominant left- and right-singular vectors and the corresponding singular value. The proposed extension assumes that the dominant singular is positive on the unit circle. The resulting algorithm is compared with a state-of-the-art PSVD algorithm and provides better accuracy with reduced computation time and lower approximation orders for the decomposition.