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Ghanbari, K., Moghaddam, M.. (1401). Construction of symmetric pentadiagonal matrix from three interlacing spectrum. فیزیولوژی و بیوتکنولوژی آبزیان, 10(2), 89-98. doi: 10.22124/jart.2022.19706.1276
K. Ghanbari; M. Rahimnevasi Moghaddam. "Construction of symmetric pentadiagonal matrix from three interlacing spectrum". فیزیولوژی و بیوتکنولوژی آبزیان, 10, 2, 1401, 89-98. doi: 10.22124/jart.2022.19706.1276
Ghanbari, K., Moghaddam, M.. (1401). 'Construction of symmetric pentadiagonal matrix from three interlacing spectrum', فیزیولوژی و بیوتکنولوژی آبزیان, 10(2), pp. 89-98. doi: 10.22124/jart.2022.19706.1276
Ghanbari, K., Moghaddam, M.. Construction of symmetric pentadiagonal matrix from three interlacing spectrum. فیزیولوژی و بیوتکنولوژی آبزیان, 1401; 10(2): 89-98. doi: 10.22124/jart.2022.19706.1276

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
مراجع
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