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

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  • Alberto, José
  • Brox, Jose

Abstract

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.

Suggested Citation

  • Alberto, José & Brox, Jose, 2020. "Inverses of k-Toeplitz matrices with applications to resonator arrays with multiple receivers," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    • Handle: RePEc:eee:apmaco:v:377:y:2020:i:c:s0096300320301545
    DOI: 10.1016/j.amc.2020.125185
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    References listed on IDEAS

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    1. Giovanni Puccetti & Christopher J. Stevens & Ugo Reggiani & Leonardo Sandrolini, 2015. "Experimental and Numerical Investigation of Termination Impedance Effects in Wireless Power Transfer via Metamaterial," Energies, MDPI, vol. 8(3), pages 1-14, March.
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