Finding optimal knots is a challenging problem in spline fitting due to a lack of prior knowledge regarding optimal knots.The unimodality of initial B-spline approximations associated with given data is a promising ch...Finding optimal knots is a challenging problem in spline fitting due to a lack of prior knowledge regarding optimal knots.The unimodality of initial B-spline approximations associated with given data is a promising characteristic of locating optimal knots and has been applied successfully.The initial B-spline approximations herein are required to approximate given data well enough and characterized by the unimodality if jumps from the highest-order derivatives of the approximations at some interior knots are local maxima.In this paper,we prove the unimodality of the initial B-spline approximations that are constructed under two assumptions:Data points are sampled uniformly and sufficiently from B-spline functions,and initial knots are chosen as the parameters of sampling points.Our work establishes the theoretical basis of the unimodality of initial B-spline approximations and pioneers the theoretical study of locating optimal knots.展开更多
There are overshoot and undershoot phenomenon and end swing phenomenon in the cubic spline fitting in Hil- bert-Huang transform. The two problems influence data quality of the empirical mode decomposition seriously. T...There are overshoot and undershoot phenomenon and end swing phenomenon in the cubic spline fitting in Hil- bert-Huang transform. The two problems influence data quality of the empirical mode decomposition seriously. The cubic spline fitting has been analysed, and the causes of producing the overshoot and undershoot phenomenon and the end swing phenomenon have been pointed out in this paper. Two new methods of cubic spline fitting and sine spline fitting and the new technique of handling the end points of the original data curve can completely re- move the overshoot and undershoot phenomenon and the end swing phenomenon on the condition of unchanging original data, and have the advantages of the continuous fitting functions and its continuous one order derivative, the simple and convenient calculations, the small calculation amount and the easy work on it.展开更多
A structured perturbation analysis of the least squares problem is considered in this paper.The new error bound proves to be sharper than that for general perturbations.We apply the new error bound to study sensitivit...A structured perturbation analysis of the least squares problem is considered in this paper.The new error bound proves to be sharper than that for general perturbations.We apply the new error bound to study sensitivity of changing the knots for curve fitting of interest rate term structure by cubic spline.Numerical experiments are given to illustrate the sharpness of this bound.展开更多
基金supported by the National Natural Science Foundation of China(No.11801393)the Natural Science Foundation of Jiangsu Province(No.BK20180831).
文摘Finding optimal knots is a challenging problem in spline fitting due to a lack of prior knowledge regarding optimal knots.The unimodality of initial B-spline approximations associated with given data is a promising characteristic of locating optimal knots and has been applied successfully.The initial B-spline approximations herein are required to approximate given data well enough and characterized by the unimodality if jumps from the highest-order derivatives of the approximations at some interior knots are local maxima.In this paper,we prove the unimodality of the initial B-spline approximations that are constructed under two assumptions:Data points are sampled uniformly and sufficiently from B-spline functions,and initial knots are chosen as the parameters of sampling points.Our work establishes the theoretical basis of the unimodality of initial B-spline approximations and pioneers the theoretical study of locating optimal knots.
基金The Foundation Research and Development Programs of China (2004CB418404).
文摘There are overshoot and undershoot phenomenon and end swing phenomenon in the cubic spline fitting in Hil- bert-Huang transform. The two problems influence data quality of the empirical mode decomposition seriously. The cubic spline fitting has been analysed, and the causes of producing the overshoot and undershoot phenomenon and the end swing phenomenon have been pointed out in this paper. Two new methods of cubic spline fitting and sine spline fitting and the new technique of handling the end points of the original data curve can completely re- move the overshoot and undershoot phenomenon and the end swing phenomenon on the condition of unchanging original data, and have the advantages of the continuous fitting functions and its continuous one order derivative, the simple and convenient calculations, the small calculation amount and the easy work on it.
基金Funds for Major State The work of the second author is partly supported by the Special Basic Research Projects(2005CB321700)the National Science Foundation of China under grant No.10571031The work of the third author is partly supported by the National Science Foundation of China under grant No.10571031.
文摘A structured perturbation analysis of the least squares problem is considered in this paper.The new error bound proves to be sharper than that for general perturbations.We apply the new error bound to study sensitivity of changing the knots for curve fitting of interest rate term structure by cubic spline.Numerical experiments are given to illustrate the sharpness of this bound.
