# Solving Cubic Matrix Equations Arising in Conservative Dynamics

@article{Benzi2021SolvingCM, title={Solving Cubic Matrix Equations Arising in Conservative Dynamics}, author={Michele Benzi and Milo Viviani}, journal={Vietnam Journal of Mathematics}, year={2021}, volume={51}, pages={113 - 126} }

In this paper we consider the spatial semi-discretization of conservative PDEs. Such finite dimensional approximations of infinite dimensional dynamical systems can be described as flows in suitable matrix spaces, which in turn leads to the need to solve polynomial matrix equations, a classical and important topic both in theoretical and in applied mathematics. Solving numerically these equations is challenging due to the presence of several conservation laws which our finite models incorporate…

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T
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### On the Consistency of the Matrix Equation $$X^\top A X=B$$ when B is Symmetric

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In this paper, which is a follow-up to Borobia et al. (Mediterr J Math, 18:40, 2021), we provide a necessary and sufficient condition for the matrix equation $$X^\top AX=B$$
X
⊤
A
X
=
B…

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