Application of nonlinear regression theory based on edge computing to mathematical modeling in universities
Mathematical modeling is the link between mathematics and practical problems and is the medium through which mathematics is widely used in related fields. This paper introduces the definitions of mathematical models in different disciplines and for different practical problems and gives the specific...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2024-01-01
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| Series: | Applied Mathematics and Nonlinear Sciences |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/amns.2023.2.00210 |
| _version_ | 1797340827964407808 |
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| author | Lu Fangfang Tao Shuang Wan Wenting |
| author_facet | Lu Fangfang Tao Shuang Wan Wenting |
| author_sort | Lu Fangfang |
| collection | DOAJ |
| description | Mathematical modeling is the link between mathematics and practical problems and is the medium through which mathematics is widely used in related fields. This paper introduces the definitions of mathematical models in different disciplines and for different practical problems and gives the specific steps of mathematical modeling and the key problems to be solved in each step, the most important of which is nonlinear regression theory. The parameter estimation of the error variance of the nonlinear regression model is performed by the least squares method, and for the problem of poor numerical stability and computational complexity due to the pathological matrix in solving the least squares method, the least squares method is proposed based on adding the edge computing framework. The results show that the system efficiency of the nonlinear regression model based on edge computing is 92%, and the resource utilization is between 80% and 90% on average, which is higher than the two algorithms of RPP and RPA. The nonlinear regression model based on edge computing proposed in this paper organically combines mathematical modeling, which can make mathematical modeling play a greater role in the practical application process and solve more practical problems. |
| first_indexed | 2024-03-08T10:09:00Z |
| format | Article |
| id | doaj.art-af4dfe640e0946cf8dfaa95780a98371 |
| institution | Directory Open Access Journal |
| issn | 2444-8656 |
| language | English |
| last_indexed | 2024-03-08T10:09:00Z |
| publishDate | 2024-01-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Applied Mathematics and Nonlinear Sciences |
| spelling | doaj.art-af4dfe640e0946cf8dfaa95780a983712024-01-29T08:52:30ZengSciendoApplied Mathematics and Nonlinear Sciences2444-86562024-01-019110.2478/amns.2023.2.00210Application of nonlinear regression theory based on edge computing to mathematical modeling in universitiesLu Fangfang0Tao Shuang1Wan Wenting2School of Mathematics and Statistics, Hubei University of Arts and Science, Xiangyang, Hubei, 441053, ChinaSchool of Mathematics and Statistics, Hubei University of Arts and Science, Xiangyang, Hubei, 441053, ChinaSchool of Mathematics and Physics, Jingchu University of Technology, JingmenHubei448000,ChinaMathematical modeling is the link between mathematics and practical problems and is the medium through which mathematics is widely used in related fields. This paper introduces the definitions of mathematical models in different disciplines and for different practical problems and gives the specific steps of mathematical modeling and the key problems to be solved in each step, the most important of which is nonlinear regression theory. The parameter estimation of the error variance of the nonlinear regression model is performed by the least squares method, and for the problem of poor numerical stability and computational complexity due to the pathological matrix in solving the least squares method, the least squares method is proposed based on adding the edge computing framework. The results show that the system efficiency of the nonlinear regression model based on edge computing is 92%, and the resource utilization is between 80% and 90% on average, which is higher than the two algorithms of RPP and RPA. The nonlinear regression model based on edge computing proposed in this paper organically combines mathematical modeling, which can make mathematical modeling play a greater role in the practical application process and solve more practical problems.https://doi.org/10.2478/amns.2023.2.00210mathematical modelingnonlinear regression modelleast squaresparameter estimationedge calculation.00a05 |
| spellingShingle | Lu Fangfang Tao Shuang Wan Wenting Application of nonlinear regression theory based on edge computing to mathematical modeling in universities Applied Mathematics and Nonlinear Sciences mathematical modeling nonlinear regression model least squares parameter estimation edge calculation. 00a05 |
| title | Application of nonlinear regression theory based on edge computing to mathematical modeling in universities |
| title_full | Application of nonlinear regression theory based on edge computing to mathematical modeling in universities |
| title_fullStr | Application of nonlinear regression theory based on edge computing to mathematical modeling in universities |
| title_full_unstemmed | Application of nonlinear regression theory based on edge computing to mathematical modeling in universities |
| title_short | Application of nonlinear regression theory based on edge computing to mathematical modeling in universities |
| title_sort | application of nonlinear regression theory based on edge computing to mathematical modeling in universities |
| topic | mathematical modeling nonlinear regression model least squares parameter estimation edge calculation. 00a05 |
| url | https://doi.org/10.2478/amns.2023.2.00210 |
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