Generalized and subset generalized bilinear models which are capable of achieving stationary for all non-linear series were developed to accommodate error process of elements of 2q-1 possible subsets with a view to achieve better model in the generalized bilinear model. The parameters of the models are estimated using robust nonlinear least-square method and Newton-Raphson iterative method. An ...

We develop a local convergence of an iterative method for solving nonlinear least squares problems with operator decomposition under the classical and generalized Lipschitz conditions. consider case both zero nonzero residuals determine their orders. use two types conditions (center restricted region conditions) to study method. Moreover, we obtain larger radius tighter error estimates than in ...

In this paper, we present some numerical studies on two partitioned fluid-structure interaction solvers: a preconditioned GMRES solver and a Newton based solver, for the fluid-structure interaction problems employing a nearly incompressible elasticity model in a classical mixed displacementpressure formulation. Both are highly relying on robust and efficient solvers for the fluid and structure ...

In this paper we present a hybrid path-following algorithm that generates inexact Newton steps suited for solving large scale and/or degenerate nonlinear programs. The algorithm uses as a central region a relaxed notion of the central path, called quasicentral path, a generalized augmented Lagrangian function, weighted proximity measures, and a linesearch within a trust region strategy. We appl...

In this chapter we present a selection of important algorithms for optimization problems with partial differential equations. The development and analysis of these methods is carried out in a Banach space setting. We begin by introducing a general framework for achieving global convergence. Then, several variants of generalized Newton methods are derived and analyzed. In particular, necessary a...

We discuss the close connection between eigenvalue computation and optimization using the Newton method and subspace methods. From the connection we derive a new class of Newton updates. The new update formulation is similar to the well-known Jacobi-Davidson method. This similarity leads to simplified versions of the Jacobi-Davidson method and the inverse iteration generalized Davidson (IIGD) m...

Sugiura, H. and T. Torii, A method for constructing generalized Runge-Kutta methods, Journal of Computational and Applied Mathematics 38 (1991) 399-410. In the implementation of an implicit Runge-Kutta formula, we need to solve systems of nonlinear equations. In this paper, we analyze the Newton iteration process and a modified Newton iteration process for solving these equations. Then we propo...