Richards’ equation and the two-phase flow equations are well-known degenerate parabolic models of air/water flow in porous media. Poor iterative solver performance and small time steps during transient simulations are often reported in field-scale simulations. In this work we study Newton-multigrid and nonlinear multigrid methods applied to discrete air/water flow models. The models are discret...

The problem of this research tackles the process of fitting two concentric spheres to data, which arises in computational metrology. There are also many fitting criteria that could be used effectively, and the most widely used one in metrology, for example, is that of the sum of squared minimal distance. However, a simple and robust algorithm assigned for using the orthogonal distance regressio...

In this paper, we derive multipoint iterative methods of fifth and sixth order for finding simple zeros of nonlinear equations. The methods are based on the composition of two steps – the first step consists of Jarratt fourth order method and the second is weighted Newton step to which correction term is applied. Per iteration each method requires two evaluations of the given function and two e...

Primal-dual interior-point methods for linear complementarity and linear programming problems solve a linear system of equations to obtain a modiied Newton step at each iteration. These linear systems become increasingly ill-conditioned in the later stages of the algorithm, but the computed steps are often suuciently accurate to be useful. We use error analysis techniques tailored to the specia...

Snap-through buckling behaviour of rigid vinyl polyethylene shallow spherical shells, undergoing large displacements, subjected to static ring loads is investigated by using finite difference and the Newton-Raphson Method. The load-deflection diagrams corresponding various values thickness, depth diameter shell with simply supported clamped edges are sketched compared. accuracy used algorithm p...

The paper provides a detailed analysis of a short step interior point algorithm applied to linear control constrained optimal control problems. Using an affine invariant local norm and an inexact Newton corrector, the well-known convergence results from finite dimensional linear programming can be extended to the infinite dimensional setting of optimal control. The present work complements a re...

We present examples of divergence for the BFGS and Gauss Newton methods. These examples have objective functions with bounded level sets and other properties concerning the examples published recently in this journal, like unit steps and convexity along the search lines. As these other examples, the iterates, function values and gradients in the new examples fit into the general formulation in ...

Two di erent time-stepping schemes are investigated for a phaseeld model of solidi cation of a pure material. A rst order accurate semiexplicit scheme which is computationally cheap per time step is compared to a more accurate fully implicit BDF-discretization. The implementation of fast Poisson and Newton-GMRES solvers are discussed in some detail. Convergence rates are experimentally validate...

We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton d...

We analyze the problem of finding a point strictly interior to a bounded, fully dimensional set from a finite dimensional Hilbert space. We generalize the results obtained for the LP, SDP and SOCP cases. The cuts added by our algorithm are central and conic. In our analysis, we find an upper bound for the number of Newton steps required to compute an approximate analytic center. Also, we provid...