| Optimization on class of operator equations in the probabilistic case setting |
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| 作者姓名： | Gen-sun FANG & Li-xin QIAN School of Mathematical Sciences Beijing Normal University Beijing China College of Mathematics and Physics Zhejiang Normal University Jinhua China |
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| 作者单位： | Gen-sun FANG & Li-xin QIAN School of Mathematical Sciences，Beijing Normal University，Beijing 100875，China College of Mathematics and Physics，Zhejiang Normal University，Jinhua 321004，China |
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| 基金项目： | 国家自然科学基金;高等学校博士学科点专项科研项目 |
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| 摘 要： | In this paper, we introduce a problem of the optimization of approximate solutions of operator equations in the probabilistic case setting, and prove a general result which connects the relation between the optimal approximation order of operator equations with the asymptotic order of the probabilistic width. Moreover, using this result, we determine the exact orders on the optimal approximate solutions of multivariate Preldholm integral equations of the second kind with the kernels belonging to the multivariate Sobolev class with the mixed derivative in the probabilistic case setting.
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Optimization on class of operator equations in the probabilistic case setting |
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| Gen-sun FANG & Li-xin QIAN School of Mathematical Sciences,Beijing Normal University,Beijing ,China College of Mathematics and Physics,Zhejiang Normal University,Jinhua ,China.Optimization on class of operator equations in the probabilistic case setting[J].Science in China(Mathematics),2007,50(1):100-104. |
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| Authors: | Gen-sun Fang Li-xin Qian |
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| Institution: | 1. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China;College of Mathematics and Physics, Zhejiang Normal University, Jinhua 321004, China |
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| Abstract: | In this paper, we introduce a problem of the optimization of approximate solutions of operator equations in the probabilistic case setting, and prove a general result which connects the relation between the optimal approximation order of operator equations with the asymptotic order of the probabilistic width. Moreover, using this result, we determine the exact orders on the optimal approximate solutions of multivariate Preldholm integral equations of the second kind with the kernels belonging to the multivariate Sobolev class with the mixed derivative in the probabilistic case setting. |
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| Keywords: | probabilistic width Gauss measure multivariate Sobolev space operator equation |
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