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A Note on the Ulmlike Method for Inverse Eigenvalue Problems
"... A Ulmlike method is proposed in [13] for solving inverse eigenvalue problems with distinct given eigenvalues. The Ulmlike method avoids solving the Jacobian equations used in Newtonlike methods and is shown to be quadratically convergent in the root sense. However, the numerical experiments in [3 ..."
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A Ulmlike method is proposed in [13] for solving inverse eigenvalue problems with distinct given eigenvalues. The Ulmlike method avoids solving the Jacobian equations used in Newtonlike methods and is shown to be quadratically convergent in the root sense. However, the numerical experiments in [3] only show that the Ulmlike method is comparable to the inexact Newtonlike method. In this short note, we give a numerical example to show that the Ulmlike method is better than the inexact Newtonlike method in terms of convergence neighborhoods. Keywords. Inverse eigenvalue problem, Ulmlike method, inexact Newtonlike method. AMS subject classifications. 65F18, 65F10, 65F15.
A Regularized Directional DerivativeBased Newton Method for Inverse Singular Value Problems
, 2012
"... In this paper, we give a regularized directional derivativebased Newton method for solving the inverse singular value problem. The proposed method is also globalized by employing the directional derivativebased Wolfe line search conditions. Under some mild assumptions, The global and quadratic co ..."
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In this paper, we give a regularized directional derivativebased Newton method for solving the inverse singular value problem. The proposed method is also globalized by employing the directional derivativebased Wolfe line search conditions. Under some mild assumptions, The global and quadratic convergence of our method is established. To improve the practical effectiveness, we also propose a hybrid method for solving the inverse singular value problem. We show that the hybrid method converges locally quadratically and globally in the sense that a stationary point of a merit function for the inverse singular value problem is computed. Numerical tests demonstrate that the proposed hybrid method is very effective for solving the inverse singular value problem with distinct and multiple singular values.