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Two New Regression and Curve Fitting Techniques Using Numerical Methods

Algorithms for Intelligent Systems, Springer Nature, 2020

Regression is a process to estimate the bond among variables. It is a statistical technique and is used as prediction with the curve fitting in machine learning, data science, economics etc. Linear and Polynomial regression is widely used to fit a curve and forecasting result. In this exploration, we propose two new linear and non-linear regression techniques using the strategy of interpolation-extrapolation and bisection of numerical analysis. However, interpolation and extrapolation cannot be applied in regression because of over fitting curve. In our paper, we have developed a technique to reduce the curve fitting that will enable the interpolation's and extrapolation's scheme to use in regression. Another procedure is to find out an equation of curve fitting with an optimal way using the Bisection Method. We also demonstrate the graphical presentations and comparison through all the occurring iterations.

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Multidimensional and Multi-Parameter Fortran-Based Curve Fitting Tools

MEJS

The Levenberg-Marquardt algorithm has become a popular method in nonlinear curve fitting works. In this paper, following the steps of Levenberg-Marquardt algorithm, we extend the framework of the algorithm to two and three dimensional real and complex functions. This work briefly describes the mathematics behind the algorithm, and also elaborates how to implement it using FORTRAN 95 programming language. The advantage of this algorithm, when it is extended to surfaces and complex functions, is that it makes researchers to have a better trust during fitting. It also improves the generalization and predictive performance of 2D and 3D real and complex functions.

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