Adaptive Generalized Eigenvector Estimating Algorithm for Hermitian Matrix Pencil

2021 ◽  
pp. 1-13
Author(s):  
Yingbin Gao
Keyword(s):  
Hermitian Matrix ◽  
Matrix Pencil ◽  
Generalized Eigenvector

scholarly journals Genus expansion of matrix models and ћ expansion of KP hierarchy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
A. Andreev ◽  
A. Popolitov ◽  
A. Sleptsov ◽  
A. Zhabin
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Special Interest ◽  
Hermitian Matrix ◽  
Geometric Meaning ◽  
Kp Hierarchy ◽  
Hurwitz Numbers ◽  
Kp Equations ◽  
Genus Expansion ◽  
Hermitian Matrix Model

Abstract We study ћ expansion of the KP hierarchy following Takasaki-Takebe [1] considering several examples of matrix model τ-functions with natural genus expansion. Among the examples there are solutions of KP equations of special interest, such as generating function for simple Hurwitz numbers, Hermitian matrix model, Kontsevich model and Brezin-Gross-Witten model. We show that all these models with parameter ћ are τ-functions of the ћ-KP hierarchy and the expansion in ћ for the ћ-KP coincides with the genus expansion for these models. Furthermore, we show a connection of recent papers considering the ћ-formulation of the KP hierarchy [2, 3] with original Takasaki-Takebe approach. We find that in this approach the recovery of enumerative geometric meaning of τ-functions is straightforward and algorithmic.

scholarly journals Locating Ships Using Time Reversal and Matrix Pencil Method by Their Underwater Acoustic Signals

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5065
Author(s):  
Daniel Chaparro-Arce ◽  
Sergio Gutierrez ◽  
Andres Gallego ◽  
Cesar Pedraza ◽  
Felix Vega ◽  
...  
Keyword(s):  
Time Reversal ◽  
Communication Channel ◽  
Matrix Pencil ◽  
Acoustic Signals ◽  
Underwater Acoustic ◽  
Low Bit Rate ◽  
Matrix Pencil Method ◽  
The Matrix ◽  
Resonance Expansion ◽  
Passive Sensors

This paper presents a technique, based on the matrix pencil method (MPM), for the compression of underwater acoustic signals produced by boat engines. The compressed signal, represented by its complex resonance expansion, is intended to be sent over a low-bit-rate wireless communication channel. We demonstrate that the method can provide data compression greater than 60%, ensuring a correlation greater than 93% between the reconstructed and the original signal, at a sampling frequency of 2.2 kHz. Once the signal was reconstituted, a localization process was carried out with the time reversal method (TR) using information from four different sensors in a simulation environment. This process sought to achieve the identification of the position of the ship using only passive sensors, considering two different sensor arrangements.

Simple Chipless RFID Sensor for Dielectric Sensing Using Shot-Time Matrix Pencil Method

2021 ◽  
Author(s):  
Sirisak Nongpromma ◽  
Akkarat Boonpoonga ◽  
Prayoot Akkaraekthalin ◽  
Lakkhana Bannawat ◽  
Titipong Lertwiriyaprapa
Keyword(s):  
Matrix Pencil ◽  
Matrix Pencil Method ◽  
Chipless Rfid
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