Estimation methods of nonlinear regression models

Donthi, Ranadheer; Prasad, S. Vijay; Mahaboob, B.; Praveen, J. Peter; Venkateswarlu, B.

doi:10.1063/1.5135256

Cited by 7 publications

(2 citation statements)

References 4 publications

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“…B.Mahaboob, 2 P.Venkateswararao, 3 P.S.Prema Kumar,4 S.Venu Madhava Sarma,5 S.Raji Reddy,6 Y.Hari Krishna,…”

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confidence: 99%

A Review Article On Mathematical Aspects Of Nonlinear Models

Mahaboob¹

2021

TURCOMAT

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The main objective of this review article is to propose some mathematical aspects of nonlinear models. In mathematics, nonlinear modelling is empirical or semi-empirical modelling which takes at least some nonlinearities into account. Nonlinear modelling in practice therefore means modelling of phenomena in which independent variables affecting the system can show complex and synergetic nonlinear effects. Contrary to traditional modelling methods, such as linear regression and basic statistical methods, nonlinear modelling can be utilized efficiently in a vast number of situations where traditional modelling is impractical or impossible. This review article mainly explores on mathematical preliminaries of nonlinear models, solution of algebraic and transcendental equations and solution of system of nonlinear equations. In addition to these Taylor polynomial and finite difference operators, least - squares polynomial approximation and the roots of the equations are also discussed here.

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“…B.Mahaboob, 2 P.Venkateswararao, 3 P.S.Prema Kumar,4 S.Venu Madhava Sarma,5 S.Raji Reddy,6 Y.Hari Krishna,…”

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confidence: 99%

A Review Article On Mathematical Aspects Of Nonlinear Models

Mahaboob¹

2021

TURCOMAT

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“…MDTM to obtain the periodic Solution of the Duffing type equations of motion, Asian Journal mathematics and Computer Research, Vol. 18…”

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confidence: 99%

Application of the Homotopy Perturbation method to solve nonlinear oscillatory differential equations

2020

IJETER

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This research article explores on the validation of homotopy perturbation procedure to solve the ordinary differential equations i) nonlinear electrical phenomenon in nonlinear inductor circuit and ii) movement of a ball bearing oscillating in bent tube with smoothness where restoring force is directly proportional to the displacement's cube. This approach gives periodic solution and period of the motion as a function of amplitude of oscillation also. The Homotopy method works very well for the cubic oscillator and good agreement of the approximate frequencies with the exact ones. The significant features of homotopy method are simplicity and its excellent accuracy for the complete range of oscillation amplitude values. This technique is very effective and convenient for solving truly nonlinear oscillatory systems. Here a comparative analysis has been made between two methods namely homotopy perturbation and the formal methods. More interestingly an isomorphism can be seen between the two methods of solution in this paper. Furthermore the uniformity of the validation of solution technique by homotopy perturbation process on entire domain has been depicted and it has been observed that the methods proposed here can be applied to strong systems which are not linear as well as for the weak systems which are considerably weak.

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Two-stage estimation and simultaneous confidence band in partially nonlinear additive model

Zhang

2021

Metrika

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Estimation methods of nonlinear regression models

Cited by 7 publications

References 4 publications

A Review Article On Mathematical Aspects Of Nonlinear Models

A Review Article On Mathematical Aspects Of Nonlinear Models

Application of the Homotopy Perturbation method to solve nonlinear oscillatory differential equations

Two-stage estimation and simultaneous confidence band in partially nonlinear additive model

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