TY - JOUR
T1 - An Extended Two-Step Method for Inverse Eigenvalue Problems with Multiple Eigenvalues
AU - Wang , Yue
AU - Shen , Weiping
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 968
EP - 992
PY - 2023
DA - 2023/11
SN - 16
DO - http://doi.org/10.4208/nmtma.OA-2023-0002
UR - https://global-sci.org/intro/article_detail/nmtma/22119.html
KW - Inverse eigenvalue problems, extended two-step method, cubic root-convergence.
AB - <p style="text-align: justify;">In recent years, numerical solutions of the inverse eigenvalue problems
with multiple eigenvalues have attracted the attention of some researchers, and
there have been a few algorithms with quadratic convergence. We propose here
an extended two-step method for solving the inverse eigenvalue problems with multiple eigenvalues. Under appropriate assumptions, the convergence analysis of the
extended method is presented and the cubic root-convergence rate is proved. Numerical experiments are provided to confirm the theoretical results and comparisons
with the inexact Cayley transform method are made. Our extended method and convergence result in the present paper may enrich the results of numerical solutions of
the inverse eigenvalue problems with multiple eigenvalues.</p>