Inverses of k-Toeplitz matrices with applications to resonator arrays with multiple receivers

We find closed-form algebraic formulas for the elements of the inverses of tridiagonal 2- and 3-Toeplitz matrices which are symmetric and have constant upper and lower diagonals. These matrices appear, respectively, as the impedance matrices of resonator arrays in which a receiver is placed over eve...

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Bibliographic Details
Published in:Applied mathematics and computation 2020-07, Vol.377, p.125185, Article 125185
Main Authors: Alberto, José, Brox, Jose
Format: Article
Language:English
Subjects:
Closed-form formulas
Currents
Determinant
Efficiency
Inverse
Multiple receivers
Resonator array
Tridiagonal k-Toeplitz matrix
Wireless power transfer
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Summary:We find closed-form algebraic formulas for the elements of the inverses of tridiagonal 2- and 3-Toeplitz matrices which are symmetric and have constant upper and lower diagonals. These matrices appear, respectively, as the impedance matrices of resonator arrays in which a receiver is placed over every 2 or 3 resonators. Consequently, our formulas allow to compute the currents of a wireless power transfer system in closed form, allowing for a simple, exact and symbolic analysis thereof. Small numbers are chosen for illustrative purposes, but the elementary linear algebra techniques used can be extended to k-Toeplitz matrices of this special form with k arbitrary, hence resonator arrays with a receiver placed over every k resonators can be analysed in the same way.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2020.125185