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National Repository of Grey Literature

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	A Hybrid Method for Nonlinear Least Squares that Uses Quasi-Newton Updates Applied to an Approximation of the Jacobian Matrix Lukšan, Ladislav ; Vlček, Jan In this contribution, we propose a new hybrid method for minimization of nonlinear least squares. This method is based on quasi-Newton updates, applied to an approximation A of the Jacobian matrix J, such that AT f = JT f. This property allows us to solve a linear least squares problem, minimizing ∥Ad+f∥ instead of solving the normal equation ATAd+JT f = 0, where d ∈ Rn is the required direction vector. Computational experiments confirm the efficiency of the new method. Detailed record
	New Quasi-Newton Method for Solving Systems of Nonlinear Equations Lukšan, Ladislav ; Vlček, Jan Fulltext: content.csg - PDF Plný tet: v1233-16 - PDF Detailed record
	O Lagrangeových multiplikátorech v metodách s lokálně omezeným krokem Lukšan, Ladislav ; Matonoha, Ctirad ; Vlček, Jan Trust-region methods are globally convergent techniques widely used, for example, in connection with the Newton's method for unconstrained optimization. One of the most commonly-used iterative approaches for solving the trust-region subproblems is the Steihaug-Toint method which is based on conjugate gradient iterations and seeks a solution on Krylov subspaces. The paper contains new theoretical results concerning properties of Lagrange multipliers obtained on these subspaces. Detailed record
	A Shifted Steihaug-Toint Method for Computing a Trust-Region Step Lukšan, Ladislav ; Matonoha, Ctirad ; Vlček, Jan Plný tet: PDF Detailed record

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