Nattapong BosuwanSouth Carolina Commission on Higher EducationMahidol University2020-06-022020-06-022020-01-01Thai Journal of Mathematics. Vol.2020, No.Special Issue (2020), 25-37168602092-s2.0-85084457186https://repository.li.mahidol.ac.th/handle/20.500.14594/56226© 2020 by the Mathematical Association of Thailand. We consider row sequences of three generalized Hermite-Padé approximations (orthogonal Hermite-Padé approximation, Hermite-Padé-Faber approximation, and multipoint Hermite-Padé approximation) of a vector of the approximated functions F and prove that if F has a system pole of order v, then such system pole attracts at least v zeros of denominators of these approximants at the rate of a geometric progression. Moreover, the rates of these attractions are estimated.Mahidol UniversityMathematicsArticleSCOPUS