Armadillo library offers iterative methods for solving nonlinear systems of equations, including the Newton-Raphson method and Broyden’s method. These techniques are useful in applications such as optimization problems, engineering simulations, and scientific computing.
The Newton-Raphson method iteratively refines an initial guess by linearizing the system at each step using Jacobian matrix approximations. It converges quadratically when close to the solution but may require good initial guesses to avoid divergence or slow convergence.
Broyden’s method is a quasi-Newton approach that updates the inverse Jacobian approximation instead of recomputing it at each iteration. This reduces computational cost while maintaining reasonable convergence properties. However, it may be less robust than Newton-Raphson in some cases.
These iterative methods can be applied in various applications like root-finding problems, parameter estimation, control systems design, and fluid dynamics simulations. They offer flexibility in handling complex, large-scale, and ill-conditioned systems where direct solvers might fail or become inefficient.
