Open AccessPERBANDINGAN SOLUSI SISTEM PERSAMAAN NONLINEAR MENGGUNAKAN METODE NEWTON-RAPHSON DAN METODE JACOBIAN
Author(s) -
Nanda Ningtyas Ramadhani Utami,
I Nyoman Widana,
Ni Made Asih
Publication year - 2013
Publication title -
e-jurnal matematika
Language(s) - English
Resource type - Journals
ISSN - 2303-1751
DOI - 10.24843/mtk.2013.v02.i02.p032
Subject(s) - jacobian matrix and determinant , newton's method , nonlinear system , mathematics , quasi newton method , steffensen's method , newton's method in optimization , iterative method , method of steepest descent , newton fractal , mathematical analysis , mathematical optimization , physics , quantum mechanics
System of nonlinear equations is a collection of some nonlinear equations. The Newton-Raphson method and Jacobian method are methods used for solving systems of nonlinear equations. The Newton-Raphson methods uses first and second derivatives and indeed does perform better than the steepest descent method if the initial point is close to the minimizer. Jacobian method is a method of resolving equations through iteration process using simultaneous equations. If the Newton-Raphson methods and Jacobian methods are compared with the exact value, the Jacobian method is the closest to exact value but has more iterations. In this study the Newton-Raphson method gets the results faster than the Jacobian method (Newton-Raphson iteration method is 5 and 58 in the Jacobian iteration method). In this case, the Jacobian method gets results closer to the exact value.