In the framework of inverse linear problems on infinite-dimensional Hilbert space, we prove convergence conjugate gradient iterates to an exact solution problem in most general case where self-adjoint, non-negative operator is unbounded and with minimal, technically unavoidable assumptions initial guess iterative algorithm. The proved always hold space norm (error convergence), as well at other...

Nonlinear conjugate gradient method is very popular in solving large-scale unconstrained minimization problems due to its simple iterative form and lower storage requirement. In the recent years, it was successfully extended to solve higher-dimension monotone nonlinear equations. Nevertheless, the research activities on conjugate gradient method in symmetric equations are just beginning. This s...

We present a practical approach for solving volume and surface mesh optimization problems. Our approach is based on Newton’s method which uses both first-order (gradient) and second-order (Hessian) derivatives of the nonlinear objective function. The volume and surface optimization algorithms are modified such that surface constraints and mesh validity are satisfied. We also propose a simple an...

In this paper, we describe an application of the planar conjugate gradient method introduced in Part 1 (Ref. 1) and aimed at solving indefinite nonsingular sets of linear equations. We prove that it can be used fruitfully within optimization frameworks; in particular, we present a globally convergent truncated Newton scheme, which uses the above planar method for solving the Newton equation. Fi...