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Session II.3 - Real-Number Complexity

Thursday, June 15, 15:00 ~ 15:30

Matrix decompositions with Newton's method

Jean-Claude Yakoubsohn

Institut de Mathématiques de Toulouse, France   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We present a general group-theoretic framework to derive efficient Newton-like iterations for the computation and certificate of various matrix decompositions, assuming that a suitable condition is known. We illustrate the approach on a list of applications, such as LU-decomposition, QR-decomposition, eigen-decomposition, singular value decomposition. This framework generalize the contents of the paper "Newton‑type methods for simultaneous matrix diagonalization" by Rima Khouja,· Bernard Mourrain and Jean‑Claude Yakoubsohn published in Calcolo(2022) 59:38.

Joint work with Joris Van der Hoeven (CNRS,LIX,Ecole Polytechnique,Palaiseau,France).

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