Rational Approximation to |<i>x</i>| at Logarithmic Nodes  

作　　者：Jiao Fang Yi Zhao Guojing Hai Jiao Fang;Yi Zhao;Guojing Hai(Department of Mathematics, Hangzhou Normal University, Hangzhou, China)

机构地区：[1]Department of Mathematics, Hangzhou Normal University, Hangzhou, China

出　　处：《Advances in Pure Mathematics》2021年第1期19-26,共8页理论数学进展（英文）

摘　　要：Based on a node group <img src="Edit_effba4ca-e855-418a-8a72-d70cb1ec3470.png" width="240" height="46" alt="" />, the Newman type rational operator is constructed in the paper. The convergence rate of approximation to a class of non-smooth functions is discussed, which is <img src="Edit_174e8f70-651b-4abb-a8f3-a16a576536dc.png" width="85" height="50" alt="" /> regarding to <em>X</em>. Moreover, if the operator is constructed based on further subdivision nodes, the convergence rate is <img src="Edit_557b3a01-7f56-41c0-bb67-deab88b9cc63.png" width="85" height="45" alt="" />. The result in this paper is superior to the approximation results based on equidistant nodes, Chebyshev nodes of the first kind and Chebyshev nodes of the second kind.Based on a node group <img src="Edit_effba4ca-e855-418a-8a72-d70cb1ec3470.png" width="240" height="46" alt="" />, the Newman type rational operator is constructed in the paper. The convergence rate of approximation to a class of non-smooth functions is discussed, which is <img src="Edit_174e8f70-651b-4abb-a8f3-a16a576536dc.png" width="85" height="50" alt="" /> regarding to <em>X</em>. Moreover, if the operator is constructed based on further subdivision nodes, the convergence rate is <img src="Edit_557b3a01-7f56-41c0-bb67-deab88b9cc63.png" width="85" height="45" alt="" />. The result in this paper is superior to the approximation results based on equidistant nodes, Chebyshev nodes of the first kind and Chebyshev nodes of the second kind.

关 键 词：Newman Type Rational Operator Logarithmic NODES Approximation Order 

分 类 号：O17[理学—数学]