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Geometrical inverse matrix approximation for least-squares problems and acceleration strategies

Abstract : We extend the geometrical inverse approximation approach to the linear least-squares scenario. For that, we focus on the minimization of 1-cos (X(A(T)A),I) , whereAis a full-rank matrix of sizemxn, with m >= n, and X is an approximation of the inverse of A(T)A. In particular, we adapt the recently published simplified gradient-type iterative scheme MinCos to the least-squares problem. In addition, we combine the generated convergent sequence of matrices with well-known acceleration strategies based on recently developed matrix extrapolation methods, and also with some line search acceleration schemes which are based on selecting an appropriate steplength at each iteration. A set of numerical experiments, including large-scale problems, are presented to illustrate the performance of the different accelerations strategies.
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https://hal-u-picardie.archives-ouvertes.fr/hal-03621846
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Soumis le : lundi 28 mars 2022 - 15:44:11
Dernière modification le : mardi 29 mars 2022 - 03:58:29

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Jean-Paul Chehab, Marcos Raydan. Geometrical inverse matrix approximation for least-squares problems and acceleration strategies. Numerical Algorithms, 2020, 85 (4), pp.1213-1231. ⟨10.1007/s11075-019-00862-z⟩. ⟨hal-03621846⟩

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