C4 interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters

Du，Jiarui1; Zhu，Yuanpeng1; Han，Xuli2

2022-11-01

10.1007/s10092-022-00487-0

CALCOLO   Impact Factor & Quartile

0008-0624

1126-5434

In this work, a class of interpolation and smoothing exponential splines with respect to a sixth order differential operator with two parameters is constructed. All the square matrices involved in the construction are proved to be tridiagonal symmetric and diagonally dominant, which results in algorithms for computing this class of exponential splines. The obtained splines have C continuity and are the minimum solution of the combination of interpolation and a generalized smoothing energy integral. The performances of the resulting splines in financial data from the S &P500 index and the effect of fitting multi-exponential decay data are given. Numerical experiments show that the resulting splines have more freedom to adjust the shape and control the energy of the curves and perform better than previous methods in fitting multi-exponential decay data. And cross validation and generalized cross validation for determining an appropriate smoothing parameter are also developed.

C4 continuity Exponential splines Sixth order differential operator Smoothing

SCI

English

Others

National Natural Science Foundation of China[11771453];Fundamental Research Funds for the Central Universities[2022ZYGXZR064];National Natural Science Foundation of China[61802129];

Mathematics

Mathematics, Applied ; Mathematics

WOS:000882392500001

SPRINGER-VERLAG ITALIA SRL

MATHEMATICS

2-s2.0-85141705164

Scopus

1.School of Mathematics,South China University of Technology,Guangdong,Guangzhou,510641,China
2.Department of Mathematics,Southern University of Science and Technology,Guangdong,Shenzhen,518055,China

Du，Jiarui,Zhu，Yuanpeng,Han，Xuli. C4 interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters[J]. CALCOLO,2022,59(4).

Du，Jiarui,Zhu，Yuanpeng,&Han，Xuli.(2022).C4 interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters.CALCOLO,59(4).

Du，Jiarui,et al."C4 interpolation and smoothing exponential splines based on a sixth order differential operator with two parameters".CALCOLO 59.4(2022).