The Solution of Non-Linear Equations System Containing Interpolation Functions by Relaxing the Newton Method


  • Nur Rokhman Universitas Gadjah Mada
  • Erwin Eko Wahyudi Universitas Gadjah Mada
  • Janoe Hendarto Universitas Gadjah Mada



non-linear equation, interpolation function, Newton method


Many world phenomena lead to nonlinear equations systems. For some applications, the non-linear equations which construct the non-linear equations system are interpolation functions. However, the interpolation functions are usually not represented as mathematical expressions but as computer programs in specific programming languages. The research proposed using the relaxed Newton method to solve the non-linear equations system that contained interpolation functions. The interpolation functions were represented in the R programming language. Then, the experiment used the Spline interpolation function to construct a two-dimensional non-linear equations system. Eleven initial guesses, maximum of ten-time iterations, and 10-7 precision were applied. The solution of the non-linear equations system and the iteration needed on each initial guess were observed. The experiment shows that the proposed method works well for solving the non-linear equations system constructed by Spline interpolation functions. By observing the initial guesses used in the experiment, there are four possible results: true solution, spurious solution, false solution, and no solution. Applying 11 initial guesses have five initial guesses resulting in true solutions, one initial guess in spurious solution, three initial guesses in false solutions, and one initial guess in no solution. The discussions imply that this method can be generalized to the three-dimensional non-linear equations system or higher dimensions.


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Author Biographies

Nur Rokhman, Universitas Gadjah Mada

Department of Computer Sciences and Electronics, Faculty of Mathematics and Natural Sciences

Erwin Eko Wahyudi, Universitas Gadjah Mada

Department of Computer Sciences and Electronics, Faculty of Mathematics and Natural Sciences

Janoe Hendarto, Universitas Gadjah Mada

Department of Computer Sciences and Electronics, Faculty of Mathematics and Natural Sciences


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