The algebraic eigenvalue problem
The algebraic eigenvalue problem
The projected gradient methods for least squares matrix approximations with spectral constraints
SIAM Journal on Numerical Analysis
SIAM Review
Computation of Gauss-Kronrod of quadrature rules
Mathematics of Computation
Robust Eigenstructure Assignment in Quadratic Matrix Polynomials: Nonsingular Case
SIAM Journal on Matrix Analysis and Applications
On robust matrix completion with prescribed eigenvalues
Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
On robust matrix completion with prescribed eigenvalues
Future Generation Computer Systems - Selected papers on theoretical and computational aspects of structural dynamical systems in linear algebra and control
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Matrix completion with prescribed eigenvalues is a special kind of inverse eigenvalue problems. Thus far, only a handful of specific cases concerning its existence and construction have been studied in the literature. The general problem where the prescribed entries are at arbitrary locations with arbitrary cardinalities proves to be challenging both theoretically and computationally. This paper investigates some continuation techniques by recasting the completion problem as an optimization of the distance between the isospectral matrices with the prescribed eigenvalues and the affine matrices with the prescribed entries. The approach not only offers an avenue to solving the completion problem in its most general setting but also makes it possible to seek a robust solution that is least sensitive to perturbation.