In this paper, we introduce a new algorithm for constructing a symmetric pentadiagonal matrix by using three interlacing spectrum, say $(\lambda_i)_{i=1}^n$, $(\mu_i)_{i=1}^n$ and $(\nu_i)_{i=1}^n$ such that \begin{eqnarray*} 0<\lambda_1<\mu_1<\lambda_2<\mu_2<...<\lambda_n<\mu_n,\\ \mu_1<\nu_1<\mu_2<\nu_2<...<\mu_n<\nu_n, \end{eqnarray*} where $(\lambda_i)_{i=1}^n$ are the eigenvalues of pentadiagonal matrix $A$, $(\mu_i)_{i=1}^n$ are the eigenvalues of $A^*$ (the matrix $A^*$ differs from $A$ only in the $(1,1)$ entry) and $(\nu_i)_{i=1}^n$ are the eigenvalues of $A^{**}$ (the matrix $A^{**}$ differs from $A^*$ only in the $(2,2)$ entry). From the interlacing spectrum, we find the first and second columns of eigenvectors. Sufficient conditions for the solvability of the problem are given. Then we construct the pentadiagonal matrix $A$ from these eigenvectors and given eigenvalues by using the block Lanczos algorithm. We also give an example to demonstrate the efficiency of the algorithm.
Ghanbari, K., & Moghaddam, M. (2022). Construction of symmetric pentadiagonal matrix from three interlacing spectrum. Journal of Algebra and Related Topics, 10(2), 89-98. doi: 10.22124/jart.2022.19706.1276
MLA
K. Ghanbari; M. Rahimnevasi Moghaddam. "Construction of symmetric pentadiagonal matrix from three interlacing spectrum". Journal of Algebra and Related Topics, 10, 2, 2022, 89-98. doi: 10.22124/jart.2022.19706.1276
HARVARD
Ghanbari, K., Moghaddam, M. (2022). 'Construction of symmetric pentadiagonal matrix from three interlacing spectrum', Journal of Algebra and Related Topics, 10(2), pp. 89-98. doi: 10.22124/jart.2022.19706.1276
VANCOUVER
Ghanbari, K., Moghaddam, M. Construction of symmetric pentadiagonal matrix from three interlacing spectrum. Journal of Algebra and Related Topics, 2022; 10(2): 89-98. doi: 10.22124/jart.2022.19706.1276
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