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A Taylor expansion of the square root matrix functional

Pierre del Moral 1 A Niclas 2 
1 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : This short note provides an explicit description of the Fréchet derivatives of the principal square root matrix functional at any order. We present an original formulation that allows to compute sequentially the Fréchet derivatives of the matrix square root at any order starting from the first order derivative. A Taylor expansion at any order with an integral remainder term is also provided, yielding the first result of this type for this class of matrix functional.
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Submitted on : Thursday, October 5, 2017 - 3:23:08 PM
Last modification on : Wednesday, February 2, 2022 - 3:54:45 PM

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  • HAL Id : hal-01593833, version 1
  • ARXIV : 1705.08561



Pierre del Moral, A Niclas. A Taylor expansion of the square root matrix functional. [Research Report] Arxiv. 2017. ⟨hal-01593833⟩



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