In the present paper, the effects of viscous dissipation and pressure stress work on free convection flow along a vertical plate have been investigated. Joule heating and heat conduction through a wall of finite thickness are considered in the investigation. With a goal to attain similarity solutions of the problem, the developed equations are made dimensionless by using suitable transformation...

The Hermitian and skew-Hermitian splitting (HSS) method is an unconditionally convergent iteration method for solving large sparse non-Hermitian positive definite system of linear equations. By making use of the HSS iteration as the inner solver for the Newton method, we establish a class of Newton-HSS methods for solving large sparse systems of nonlinear equations with positive definite Jacobi...

Non-linear image reconstruction methods are desirable for applications in electrical impedance tomography (EIT) such as brain or breast imaging where the assumptions of linearity are violated. We present a novel non-linear Newton-Krylov method for solving large-scale EIT inverse problems, which has the potential advantages of improved robustness and computational efficiency over previous method...

Image registration is often very slow because of the high dimensionality of the images and complexity of the algorithms. Adaptive stochastic gradient descent (ASGD) outperforms deterministic gradient descent and even quasi-Newton in terms of speed. This method, however, only exploits first-order information of the cost function. In this paper, we explore a stochastic quasi-Newton method (s-LBFG...

This thesis discusses strategies for numerically solving a two dimensional integral. The difficulties here are due to numerous integrands and regions in R2. The transformation to units as the 2-simplex and the cube can simplify many integrands. An approach to arbitrary regions is to decompose them into easy ones as triangles and rectangles. For these regions formulas that approximate the two di...