| The best quadrature formula based on Hermite information for the class KW~2[a,b] |
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| 作者姓名： | WANG Xinghua~ |
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| 作者单位： | 1，2 |
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| 基金项目： | 国家重点基础研究发展计划(973计划)，国家自然科学基金 |
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| 摘 要： | The best quadrature formula has been found in the following sense:for afunction whose norm of the second derivative is bounded by a given constant and thebest quadrature formula for the approximate evaluation of integration of that function canminimize the worst possible error if the values of the function and its derivative at certainnodes are known.The best interpolation formula used to get the quadrature formula aboveis also found.Moreover,we compare the best quadrature formula with the open compoundcorrected trapezoidal formula by theoretical analysis and stochastic experiments.
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The best quadrature formula based on Hermite information for the class KW2[a,b] |
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| WANG Xinghua.The best quadrature formula based on Hermite information for the class KW~2[a,b][J].Science in China(Mathematics),2005,48(1). |
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| Authors: | WANG Xinghua MI Xiangjiang |
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| Institution: | 1. Department of Mathematics,Zhejiang University,Hangzhou 310028,China;College of Mathematics and Infomation Science,Wenzhou University,Wenzhou 325003,China
2. Department of Mathematics,Zhejiang University,Hangzhou 310028,China |
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| Abstract: | The best quadrature formula has been found in the following sense:for afunction whose norm of the second derivative is bounded by a given constant and thebest quadrature formula for the approximate evaluation of integration of that function canminimize the worst possible error if the values of the function and its derivative at certainnodes are known.The best interpolation formula used to get the quadrature formula aboveis also found.Moreover,we compare the best quadrature formula with the open compoundcorrected trapezoidal formula by theoretical analysis and stochastic experiments. |
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| Keywords: | class of second differentiable functions Hermite information best quadrature formula best interpolation method stochastic experiment open compound corrected trapezoidal formula Iyengar-type inequalities |
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