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  • A MEMORYLESS SYMMETRIC RANK-ONE METHOD WITH SUFFICIENT DESCENT PROPERTY FOR UNCONSTRAINED OPTIMIZATION

    Nakayama Shummin , Narushima Yasushi , Yabe Hiroshi

    … Recently, several researchers studied the memoryless quasi-Newton method based on the symmetric rank-one formula. … However existing memoryless symmetric rank-one methods do not necessarily satisfy the sufficient descent condition. …

    Journal of the Operations Research Society of Japan 61(1), 53-70, 2018

    J-STAGE 

  • Real Shintani Functions on U(n,1)

    Tsuzuki Masao

    … We realize $H$ as a closed subgroup of $G$, so that $(G,H)$ forms a semisimple symmetric pair of rank one. … We prove that ${\rm dim}_\C{\cal I}_{η,π}\leqslant 1$ for any $π $ and any $η$, giving an explicit formula of the Shintani functions that generate a \lq corner\rq\ $K$-type of $π$ in terms of Gaussian hypergeometric series. … We also give an explicit formula of corner $K$-type matrix coefficients of $π$ in the usual sense. …

    Journal of mathematical sciences, the University of Tokyo 8(4), 609-688, 2001

    IR 

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