Contractions on Riemannian...(ICCT 2020, 2020.07.08-07.10) > 자유게시판

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논문명

​Contractions on Riemannian manifolds and nonlinear matrix equations 

Abstract 

​In this talk we consider the semigroup generated by the self-maps on the open convex cone of positive definite matrices of translations, congruence transformations and matrix inversion that includes symplectic Hamiltonians and show that every member of the semigroup contracts any invariant metric distance inherited from a symmetric gauge function. This extends the results of Bougerol for the Riemannian metric and of Liverani–Wojtkowski for the Thompson part metric. A uniform upper bound of the Lipschitz contraction constant for a member of the semigroup is given in terms of the minimum eigenvalues of its determining matrices. We apply this result to a variety of nonlinear equations including Stein and Riccati equations for uniqueness and existence of positive definite solutions and find a new convergence analysis of iterative algorithms for the positive definite solution depending only on the least contraction coefficient for the invariant metric from the spectral norm.

논문 정보 

Hosoo Lee

Prof., Dept. of Mathematics Education., Teachers College, Jeju Natl. University, Korea

hosoo@jejunu.ac.kr

The 10th International Conference on Convergence Technology in 2020

July 8 ~ July 10, 2020 Jeju National University, Jeju, Korea