A two-step Ulm-Chebyshev-like Cayley transform method for inverse eigenvalue problems with multiple eigenvalues

Wei Ma; Zhenhao Li; Yuxin Zhang; Wei Ma; Zhenhao Li; Yuxin Zhang

doi:10.3934/math.20241117

AIMS Mathematics

2024, Volume 9, Issue 8: 22986-23011. doi: 10.3934/math.20241117

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Research article

A two-step Ulm-Chebyshev-like Cayley transform method for inverse eigenvalue problems with multiple eigenvalues

1.
School of Mathematics and Statistics, Nanyang Normal University, Nanyang, Henan 473061, China
2.
School of Artificial Intelligence and Software Engineering, Nanyang Normal University, Nanyang, Henan 473061, China

Received: 27 May 2024 Revised: 12 July 2024 Accepted: 15 July 2024 Published: 25 July 2024
MSC : 15A18, 65F15, 65F18

Our focus in this study was on examining the convergence problem of a novel method, inspired by the Ulm-Chebyshev-like Cayley transform method, which was designed to solve the inverse eigenvalue problems (IEPs) with multiple eigenvalues. Compared with other existing methods, the proposed method has higher convergence order and/or requires less operations. Under the assumption that the relative generalized Jacobian matrices at a solution are nonsingular, the proposed method was proved to be convergent with cubic convergence. Experimental findings demonstrated the practicality and efficiency of the suggested approaches.
- inverse eigenvalue problems,
- multiple eigenvalues,
- Ulm-Chebyshev-like method,
- Cayley transform,
- cubically convergent
Citation: Wei Ma, Zhenhao Li, Yuxin Zhang. A two-step Ulm-Chebyshev-like Cayley transform method for inverse eigenvalue problems with multiple eigenvalues[J]. AIMS Mathematics, 2024, 9(8): 22986-23011. doi: 10.3934/math.20241117

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Abstract

Our focus in this study was on examining the convergence problem of a novel method, inspired by the Ulm-Chebyshev-like Cayley transform method, which was designed to solve the inverse eigenvalue problems (IEPs) with multiple eigenvalues. Compared with other existing methods, the proposed method has higher convergence order and/or requires less operations. Under the assumption that the relative generalized Jacobian matrices at a solution are nonsingular, the proposed method was proved to be convergent with cubic convergence. Experimental findings demonstrated the practicality and efficiency of the suggested approaches.

References

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