A significant portion of the time required for simulating full three-dimensional (3D) charge transport in semiconductor devices using particle-based methods is spent solving the necessary field equations. Two highly effective, iterative techniques available for solving largesparse systems of equations are the conjugate gradient (CG) method and the multigrid (MG) method. In this work, variants o...

In this paper, we seek the conjugate gradient direction closest to the direction of the scaled memoryless BFGS method and propose a family of conjugate gradient methods for unconstrained optimization. An improved Wolfe line search is also proposed, which can avoid a numerical drawback of the Wolfe line search and guarantee the global convergence of the conjugate gradient method under mild condi...

The natural gradient method has been used effectively in conjugate Gaussian process models, but the non-conjugate case has been largely unexplored. We examine how natural gradients can be used in non-conjugate stochastic settings, together with hyperparameter learning. We conclude that the natural gradient can significantly improve performance in terms of wall-clock time. For illconditioned pos...

.. ................................................................................................................... ix Chapter 1. Introduction ..................................................................................................1 Chapter 2. Background ..................................................................................................6 2.1. Matrix Compu...

The computational burden of primal-dual interior point methods for linear programming relies on the computation of the search direction by solving one or more linear systems per iterations. The objective of this work is to study an efficient and robust way of solving these systems for large-scale sparse problems. Our proposal combines the use of the stable system and a hybrid iterative method w...

A new method used to prove the global convergence of the nonlinear conjugate gradient methods, the spectral method, is presented in this paper, and it is applied to a new conjugate gradient algorithm with sufficiently descent property. By analyzing the descent property, several concrete forms of this algorithm are suggested. Under standard Wolfe line searches, the global convergence of the new ...

With the innovation of cloud computing industry lots of services were provided based on different deployment criteria. Nowadays everyone tries to remain connected and demand maximum utilization of resources with minimum timeand effort. Thus, making it an important challenge in cloud computing for optimum utilization of resources. To overcome this issue, many techniques have been proposed ...