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

2024

AIMS Mathematics, Vol 9, Iss 8, Pp 22986-23011 (2024)

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.

article

English

AIMS Press, 2024.

inverse eigenvalue problems, multiple eigenvalues, ulm-chebyshev-like method, cayley transform, cubically convergent, Mathematics, QA1-939