| Numerical integral formula of two-dimension based on optimal approximation |
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| 作者姓名： | 吴勃英 王勇 |
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| 作者单位： | Dept. of Mathematics，Harbin Institute of Technology，Harbin 150001，China |
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| 基金项目： | SponsoredbytheNaturalScienceFoundationofHeilongjiangProvinceandtheScientificResearchFoundationofHarbinInstituteofTechnology(GrantNo.HIT.MD2001.26). |
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| 摘 要： | 1 ＲＥＰＲＯＤＵＣＩＮＧＫＥＲＮＥＬＳＰＡＣＥＡＮＤＩＴＳＲＥＰＲＯＤＵＣＩＮＧＫＥＲＮＥＬＦｏｒｃｏｎｖｅｎｉｅｎｃｅ ,ｗｉｔｈｏｕｔｌｏｓｓｏｆｇｅｎｅｒａｌｉｔｙ ,ｗｅｌｅｔＤ =0 ,1]× 0 ,1].ＳｕｐｐｏｓｅＨ2 ={ｕ(ｘ ,ｙ) ｜ ｕ ｘ, ｕ ｙａｒｅｃｏｍｐｌｅｔｅｌｙｃｏｎ ｔｉｎｕｏｕｓｆｕｎｃｔｉｏｎｓｉｎＤ , αｕ ｘα1 ｙα2 ∈Ｌ2 (Ｄ) ,α=α1+α2 ,αｉ=0 ,1,2 ,ｉ=1,2 } ,ｆｏｒａｎｙｕ ,ｖ ∈Ｈ2 ,ｗｅｄｅｆｉｎｅｉｎｎｅｒｐｒｏｄｕｃｔ(ｕ ,ｖ) = Ｄ(ｕｖ+ 2 ｕ ｘ ｖ ｘ + 2 ｕ ｙ ｖ…
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Numerical integral formula of two-dimension based on optimal approximation |
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| WU Bo-ying,WANG Yong.Numerical integral formula of two-dimension based on optimal approximation[J].Journal of Harbin Institute of Technology,2002,9(2). |
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| Authors: | WU Bo-ying WANG Yong |
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| Abstract: | There are such problems as convergence and stability of numerical calculations during multivariate interpolation. Moreover, it is very difficult to construct a overall multivariate numerical interpolation formula to ensure convergence for a set of irregular nodes. In this paper by means of an optimal binary interpolation formula given in a reproducing kernel space, a high precision overall two dimension numerical integral formula is established and its advantage is that it ensures the convergence for arbitrary irregular node set in the integral domain. |
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| Keywords: | optimal approximation numerical integral formula convergence and stability |
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