In addition, novel adaptations have extended these methods to tackle large-scale nonlinear equations and image restoration challenges, demonstrating both robustness and computational efficiency [3].

We describe a preconditioned linear conjugate-gradient method that defines a search direction which interpolates between the direction defined by a nonlinear conjugate-gradient-type algorithm and a ...

The trust region method performs well for small- to medium-sized problems, and it does not need many function, gradient, and Hessian calls. However, if the computation of the Hessian matrix is ...

Conventional numerical methods for the solution of FWI problems are gradient-based methods, such as the preconditioned steepest descent, the nonlinear conjugate gradient, or more recently the l-BFGS ...

Conjugate gradient methods form a class of iterative algorithms that are highly effective for solving large‐scale unconstrained optimisation problems.