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<p>This study introduces a relationship between the Chebyshev polynomial and the matrix-less method. In this way, it explains the roots of the Chebyshev polynomial and their role in the theory of matrix polynomials. With the help of these techniques, we can evaluate the determinant of some band matrices and pay special attention to the polynomial eigenvalue problem for matrix polynomials expressed in the nonmonomial bases. Numerical results are presented and compared with corresponding theoretical data.</p>

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A review for finding determinants of some band matrices

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Maryam Shams Solary

摘要

This study introduces a relationship between the Chebyshev polynomial and the matrix-less method. In this way, it explains the roots of the Chebyshev polynomial and their role in the theory of matrix polynomials. With the help of these techniques, we can evaluate the determinant of some band matrices and pay special attention to the polynomial eigenvalue problem for matrix polynomials expressed in the nonmonomial bases. Numerical results are presented and compared with corresponding theoretical data.