NewtonRaphsonbased
NewtonRaphsonbased is a term used to describe methods and algorithms that rely on the Newton-Raphson iteration as the core computational step for solving equations or optimizing functions.
In the univariate case, given a differentiable function f, the iteration is x_{n+1} = x_n - f(x_n)/f'(x_n). This
In multiple dimensions, the approach solves F(x) = 0 using x_{k+1} = x_k - J_F(x_k)^{-1} F(x_k), where F is
Convergence is quadratic near a simple root, provided the derivative (or Jacobian) is well-behaved and the initial
Applications in science and engineering include root finding, solving nonlinear systems, computing equilibria, and optimization problems