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Kondo, Koichi
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Astronomy Chemistry Earth & Planetary Sciences Mathematics Physics

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An Algorithm to Construct a Tridiagonal Matrix Factored by Bidiagonal Matrices with Prescribed Eigenvalues and Specified Entries Kondo, Koichi
Journal of Mathematical and Fundamental Sciences Vol. 56 No. 3 (2024)
Publisher : Directorate for Research and Community Services (LPPM) ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/j.math.fund.sci.2024.56.3.5

Abstract

This paper presents an algorithm to construct a tridiagonal matrix factored by bidiagonal matrices with prescribed eigenvalues and specified matrix entries. The proposed algorithm addresses inverse eigenvalue problems (IEPs) constrained by LR decomposition. Using techniques from discrete soliton theory, we derive recurrence relations that connect matrix entries and eigenvalues. The algorithm systematically computes unknown entries in the matrix from given spectrum data and partial matrix information. Several examples, including cases with real, complex, and multiple eigenvalues, demonstrate the efficiency of the proposed algorithm. Additionally, we provide conditions under which the algorithm successfully solves the IEP.
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