TITLE:
Rational Approximation to |x| at Logarithmic Nodes
AUTHORS:
Jiao Fang, Yi Zhao, Guojing Hai
KEYWORDS:
Newman Type Rational Operator, Logarithmic, Nodes, Approximation Order
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.11 No.1,
January
21,
2021
ABSTRACT: Based on a node group , 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 regarding to X. Moreover, if the operator is constructed based on further subdivision nodes, the convergence rate is . 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.