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Article Dans Une Revue Calcolo Année : 2022

Newton-Type Methods For Simultaneous Matrix Diagonalization

Résumé

This paper proposes a Newton-type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable system of equations associated to this problem, we construct a sequence that converges quadratically towards the solution. This construction is not based on the resolution of a linear system as is the case in the classical Newton method. Moreover, we provide a theoretical analysis of this construction and exhibit a condition to get a quadratic convergence. We also propose numerical experiments, which illustrate the theoretical results.
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Dates et versions

hal-03390265 , version 1 (21-10-2021)
hal-03390265 , version 2 (03-11-2022)

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Rima Khouja, Bernard Mourrain, Jean-Claude Yakoubsohn. Newton-Type Methods For Simultaneous Matrix Diagonalization. Calcolo, 2022, ⟨10.1007/s10092-022-00484-3⟩. ⟨hal-03390265v2⟩
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