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Approximating Eigenvalues of a Class of Perturbed Tridiagonal Systems

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  • Christos Chorianopoulos

    (TelSiP Laboratory, Department of Electrical and Electronics Engineering, University of West Attica, 12244 Egaleo, Greece)

  • Ioannis Th. Famelis

    (microSENSES Laboratory, Department of Electrical and Electronics Engineering, University of West Attica, 12244 Egaleo, Greece)

Abstract

We study a class of perturbed tridiagonal problems in the form of a rank-one update of a symmetric tridiagonal Toeplitz matrix. We derive computable formulas for up to eighth-order polynomial approximations or closed formulas for quartic approximation. Moreover, we study some symmetries that characterise the coefficients of these polynomials. Numerical testing suggested that the error is close to machine accuracy in the former case and surprising low in the latter, whereas for big matrices the computational time is clearly lower compared to the MATLAB’s eig function.

Suggested Citation

  • Christos Chorianopoulos & Ioannis Th. Famelis, 2026. "Approximating Eigenvalues of a Class of Perturbed Tridiagonal Systems," Mathematics, MDPI, vol. 14(6), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:6:p:1063-:d:1900262
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