The Newton-Raphson method is used to iteratively refine the solution to a system of nonlinear equations. The Jacobian matrix, representing the system's sensitivity to changes in variables, is ...

Many authors suggested methods to solve nonlinear equations. Each of these methods has its advantages and disadvantages. In this work, we chose some methods with low cost and high accuracy such as ...

where J(x) is the Jacobian matrix of partial derivatives of F with respect to x. For optimization problems, the same method is used, where F(x) is the gradient of the objective function and J(x) ...

Description: The Newton-Raphson method is an iterative numerical technique used for solving systems of nonlinear equations. In the context of power systems, it is often employed to solve the nonlinear ...

This expository paper traces the development of the Newton-Raphson method for solving nonlinear algebraic equations through the extant notes, letters, and publications of Isaac Newton, Joseph Raphson, ...

ABSTRACT: We propose and demonstrate an original geometric argument for the ancient Babylonian square root method, which is analyzed and compared to the Newton-Raphson method. Based on simple geometry ...

Article citations More>> Grau-Sánchez, M. and Daz-Barrero, J.L. (2011) A Technique to Composite a Modified Newton’s Method for Solving Nonlinear Equations. ArXiv e-prints. has been cited by the ...