Constructing symmetric nonnegative matrices with prescribed eigenvalues by differential equations
SIAM Journal on Mathematical Analysis
SIAM Review
A Numerical Method for the Inverse Stochastic Spectrum Problem
SIAM Journal on Matrix Analysis and Applications
Numerical Methods for Solving Inverse Eigenvalue Problems for Nonnegative Matrices
SIAM Journal on Matrix Analysis and Applications
A descent method for structured monotone variational inequalities
Optimization Methods & Software
Isospectral flow method for nonnegative inverse eigenvalue problem with prescribed structure
Journal of Computational and Applied Mathematics
Solving Large-Scale Least Squares Semidefinite Programming by Alternating Direction Methods
SIAM Journal on Matrix Analysis and Applications
Nonnegative inverse eigenvalue problems with partial eigendata
Numerische Mathematik
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We consider the nonnegative inverse eigenvalue problem with partial eigendata, which aims to find a nonnegative matrix such that it is nearest to a pre-estimated nonnegative matrix and satisfies the prescribed eigendata. In this paper, we propose several iterative schemes based on the alternating direction method of multipliers for solving the nonnegative inverse problem. We also extend our schemes to the symmetric case and the cases of prescribed lower bounds and of prescribed entries. Numerical tests (including a practical engineering application in vibrations) show the efficiency of the proposed iterative schemes.