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.
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
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.
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