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arXiv · 2110.11133

Newton-Type Methods For Simultaneous Matrix Diagonalization

Rima Khouja·Bernard Mourrain·Jean-Claude Yakoubsohn
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Abstract

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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Rima Khouja, Bernard Mourrain, Jean-Claude Yakoubsohn. 2021-10-21. Newton-Type Methods For Simultaneous Matrix Diagonalization. https://doi.org/0.1007/s10092-022-00484-3

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