# Solving Nonlinear Equation Systems

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## Abstract

This chapter deals with solving nonlinear equation systems that describe the computational models for tapered and cylinder roller bearings in Chaps. 1 and 2. In general, the computational models consisting of a large number of coupled equations are strongly nonlinear. It is not easy to get converged solutions for large strongly nonlinear coupled equation systems. Therefore, an appropriate algorithm is required to solve such nonlinear equation systems. In the following sections, the Gauss-Newton and the Levenberg-Marquardt algorithm based on least squares method are mathematically derived for solving the computational models of tapered and cylinder roller bearings.

## References

- 1.Nguyen-Schäfer, H., Schmidt, J.P.: Tensor Analysis and Elementary Differential Geometry for Physicists and Engineers, 2nd edn. Springer, Berlin, Heidelberg (2017)CrossRefGoogle Scholar
- 2.Quarteroni, A., Saleri, F., Gervasio, P.: Scientific Computing with MATLAB and Octave, 4th edn. Springer, Berlin, Heidelberg (2014)CrossRefGoogle Scholar
- 3.Nguyen-Schäfer, H.: Computational Design of Rolling Bearings. Springer International Publishing, Switzerland (2016)CrossRefGoogle Scholar
- 4.Antia, H.M.: Numerical Methods for Scientists and Engineers, 2nd edn. Birkhäuser, Basel-Boston-Berlin (2002)zbMATHGoogle Scholar

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