Approximating Eigenvalues of a Class of Perturbed Tridiagonal Systems
Year: 2026
Type: article
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.
Source: Mathematics
DOI: 10.3390/math14061063
Institution: University of West Attica
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7140115151
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