Multivariate function approximations using the D-MORPH algorithm
Most real-life problems are computationally burdensome and time consuming, so we have to rely on approximate functions to represent the original functions with a specific level of accuracy. In this study, we propose a new method for approximating multivariate functions based on the diffeomorphic mod...
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| Vydané v: | Applied mathematical modelling Ročník 39; číslo 23-24; s. 7155 - 7180 |
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| Hlavní autori: | , |
| Médium: | Journal Article |
| Jazyk: | English |
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Elsevier Inc
01.12.2015
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| ISSN: | 0307-904X |
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| Abstract | Most real-life problems are computationally burdensome and time consuming, so we have to rely on approximate functions to represent the original functions with a specific level of accuracy. In this study, we propose a new method for approximating multivariate functions based on the diffeomorphic modulation under observable response preserving homotopy (D-MORPH) algorithm. D-MORPH is a regression technique that was originally developed for solving differential equation. Two distinct approaches using the proposed method are described, where one operates over the whole domain and the other operates by sub-dividing the domain into a finite number of sub-domains. This technique is based on a cost/objective function, which depends on a weight matrix. We also introduce a new weight matrix, which dramatically reduces the prediction error and improves the prediction accuracy. The potential of the proposed approach for approximating multivariate functions is illustrated using eight mathematical functions and two practical problems. Furthermore, a comparative assessment with other methods is provided to demonstrate the elegance of the proposed method. |
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| AbstractList | Most real-life problems are computationally burdensome and time consuming, so we have to rely on approximate functions to represent the original functions with a specific level of accuracy. In this study, we propose a new method for approximating multivariate functions based on the diffeomorphic modulation under observable response preserving homotopy (D-MORPH) algorithm. D-MORPH is a regression technique that was originally developed for solving differential equation. Two distinct approaches using the proposed method are described, where one operates over the whole domain and the other operates by sub-dividing the domain into a finite number of sub-domains. This technique is based on a cost/objective function, which depends on a weight matrix. We also introduce a new weight matrix, which dramatically reduces the prediction error and improves the prediction accuracy. The potential of the proposed approach for approximating multivariate functions is illustrated using eight mathematical functions and two practical problems. Furthermore, a comparative assessment with other methods is provided to demonstrate the elegance of the proposed method. |
| Author | Chakraborty, Souvik Chowdhury, Rajib |
| Author_xml | – sequence: 1 givenname: Souvik surname: Chakraborty fullname: Chakraborty, Souvik email: csouvik41@gmail.com – sequence: 2 givenname: Rajib surname: Chowdhury fullname: Chowdhury, Rajib email: rajibfce@iitr.ac.in |
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| Keywords | Weight matrix Multivariate polynomial D-MORPH Objective function |
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