Study on the Curvature Reducing Method of Non-linear Regression Model

摘要

The method to reduce the non-linear strength (curvature)of non-linear regression model was studied in this paper. Firstly, the reference point of the non-linear strength was analyzed. Based on the definition of curvature cubic matrix, a computing method of curvature cubic matrix was proposed based on the Cholesky disassembling. Then the common ways to reduce the non-linear strength was also discussed. Pointed at some common non-linear models in real engineering applications, such as non-linear models used for multiple-measurement and mutual-calibration of different instruments, or non-linear models prior information, a new least square method with weight was given, which can evidently reduce the curvature of these multi-structure non-linear regression models, therefore evidently reduce the non-linear strength. Finally, the Numerical simulation results were given to validate the effectiveness and feasibility of this weighted least square method. The method to reduce the non-linear strength (curvature) of non-linear regression model was studied in this paper. Firstly, the reference point of the non-linear strength was analyzed. Based on the definition of curvature cubic matrix, a computing method of curvature cubic matrix was proposed based on the Cholesky disassembling. Then the common ways to reduce the non-linear strength was also discussed. Pointed at some common non-linear models in real engineering applications, such as non-linear models used for multiple-measurement and mutual-calibration of different instruments, or non-linear models with prior informations, a new least square method with weight was given, which can evidently reduce the curvature of these multi-structure non-linear regression models, therefore evidently reduce the non-linear strength. Finally, the Numerical simulation results ware given to validated the effectiveness and feasibility of this weighted least square method.Key words: Non-linear regression / curvature / cholesky disassembling / least square with weight