| ON THE CONVERGENCE OF PADE-TYPE APPROXIMANTS IN TWO VARIABLES |
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| 作者姓名： | 朱功勤 朱晓临 |
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| 作者单位： | Department of Applied Math. &Mech. Hefei University of Technology，Hefei 230009，PRC.，Department of Applied Math. &Mech. Hefei University of Technology，Hefei 230009，PRC. |
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| 摘 要： | In 1], C. Brezinski raised three unsolved questions in studing multivariable Pade-iype approximation, and the convergence of multivariable Pade-iype approximants under the general conditions is one of them. We have only seen in 2] that the convergence of the mullivariable Fade-type approximants is discussed for a kind of functions defined by Stieltjes integrations under some special conditions. However, the general convergence theorem has not been seen so far. In this paper, some error formulae of bivariate Fade-type approximants in in-legral form are given. By virtue of them, a number of convergence theorems of bivariate Pade-iype approximants are proved under general conditions.
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ON THE CONVERGENCE OF PADE-TYPE APPROXIMANTS IN TWO VARIABLES |
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| Zhu Gong-qin.ON THE CONVERGENCE OF PADE-TYPE APPROXIMANTS IN TWO VARIABLES[J].Numerical Mathematics A Journal of Chinese Universities English Series,1993(2). |
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| Authors: | Zhu Gong-qin |
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| Institution: | Zhu Gong-qin Department of Applied Math. &Mech. Hefei University of Technology,Hefei 230009,PRC.Zhu Xiao-lin Department of Applied Math. &Mech. Hefei University of Technology,Hefei 230009,PRC. |
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| Abstract: | In 1], C. Brezinski raised three unsolved questions in studing multivariable Pade-iype approximation, and the convergence of multivariable Pade-iype approximants under the general conditions is one of them. We have only seen in 2] that the convergence of the mullivariable Fade-type approximants is discussed for a kind of functions defined by Stieltjes integrations under some special conditions. However, the general convergence theorem has not been seen so far. In this paper, some error formulae of bivariate Fade-type approximants in in-legral form are given. By virtue of them, a number of convergence theorems of bivariate Pade-iype approximants are proved under general conditions. |
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| Keywords: | Bivariate Pade-type approximanls error formula convergence |
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