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Construction of symmetric pentadiagonal matrix from three interlacing spectrum | ||
| Journal of Algebra and Related Topics | ||
| دوره 10، شماره 2، اسفند 2022، صفحه 89-98 اصل مقاله (267.63 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2022.19706.1276 | ||
| نویسندگان | ||
| K. Ghanbari* 1؛ M. Rahimnevasi Moghaddam2 | ||
| 1Department of Mathematics, Sahand University of Technology, Tabriz, IRAN | ||
| 2Department of Mathematics, Sahand University of Technology, Tabriz, Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Inverse eigenvalue problem؛ Pentadiagonal matrix؛ Interlacing property؛ Lanczos algorithm | ||
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آمار تعداد مشاهده مقاله: 109 تعداد دریافت فایل اصل مقاله: 209 |
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