• 论文 •

### 非光滑函数的分数阶插值公式

1. 天津师范大学数学科学学院, 天津 300387
• 收稿日期:2015-12-07 出版日期:2016-04-15 发布日期:2016-05-13
• 基金资助:

国家自然科学基金(11471166)资助项目.

Fan Meng, Wang Tongke, Chang Huibin. A FRACTIONAL INTERPOLATION FORMULA FOR NON-SMOOTH FUNCTIONS[J]. Mathematica Numerica Sinica, 2016, 38(2): 212-224.

### A FRACTIONAL INTERPOLATION FORMULA FOR NON-SMOOTH FUNCTIONS

Fan Meng, Wang Tongke, Chang Huibin

1. School of Mathematical Sciences, Tianjin Normal University, Tianjin 300387, China
• Received:2015-12-07 Online:2016-04-15 Published:2016-05-13

This paper constructs a fractional interpolation formula for non-smooth functions based on the local fractional Taylor's expansion. The existence and uniqueness of the fractional interpolation formula are proved. The formula with Lagrange basis and its error remainder are provided. The convergence order of a hybrid pattern for piecewise fractional order interpolation and integer-order interpolation is also discussed. Numerical examples demonstrate that the fractional interpolation is obviously superior to the traditional polynomial interpolation for non-smooth functions. They also show that the interpolating error can be uniformly distributed on the interval by using the piecewise hybrid interpolation, which can exceedingly improve the interpolation accuracy.

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