Newton-conjugate-gradient methods for solitary wave computations

Newton-conjugate-gradient methods for solitary wave computations

In this paper, the Newton-conjugate-gradient methods are developed for solitary wave computations. These methods are based on Newton iterations, coupled with conjugategradient iterations to solve the resulting linear Newton-correction equation. When the linearization operator is self-adjoint, the preconditioned conjugate-gradient method is proposed to solve this linear equation. If the lineariz...

Multilevel Conjugate Gradient Methods

Preconditioned Conjugate Gradient Methods in Truncated Newton Frameworks for Large-scale Linear Classification

Truncated Newton method is one of the most effective optimization methods for large-scale linear classification. The main computational task at each Newton iteration is to approximately solve a quadratic sub-problem by an iterative procedure such as the conjugate gradient (CG) method. It is known that CG has slow convergence if the sub-problem is ill-conditioned. Preconditioned CG (PCG) methods...

Novel preconditioners based on quasi-Newton updates for nonlinear conjugate gradient methods

In this paper we study new preconditioners to be used within the Nonlinear Conjugate Gradient (NCG) method, for large scale unconstrained optimization. The rationale behind our proposal draws inspiration from quasi– Newton updates, and its aim is to possibly approximate in some sense the inverse of the Hessian matrix. In particular, at the current iteration of the NCG we consider some precondit...

Application of frames in Chebyshev and conjugate gradient methods

‎Given a frame of a separable Hilbert space $H$‎, ‎we present some‎ ‎iterative methods for solving an operator equation $Lu=f$‎, ‎where $L$ is a bounded‎, ‎invertible and symmetric‎ ‎operator on $H$‎. ‎We present some algorithms‎ ‎based on the knowledge of frame bounds‎, ‎Chebyshev method and conjugate gradient method‎, ‎in order to give some‎ ‎approximated solutions to the problem‎. ‎Then we i...