Accelerated Inexact Newton Schemes for Large Systems of Nonlinear Equations

Solving systems of nonlinear equations using decomposition technique

A systematic way is presented for the construction of multi-step iterative method with frozen Jacobian. The inclusion of an auxiliary function is discussed. The presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of Newton multi-step method. The auxiliary function provides us the way to overcome the singul...

Inexact Newton Methods Applied to Under – Determined Systems by Joseph P . Simonis A Dissertation

Consider an under-determined system of nonlinear equations F (x) = 0, F : IR → IR, where F is continuously differentiable and m > n. This system appears in a variety of applications, including parameter–dependent systems, dynamical systems with periodic solutions, and nonlinear eigenvalue problems. Robust, efficient numerical methods are often required for the solution of this system. Newton’s ...

Accelerated Inexact Newton Schemes for Largesystems of Nonlinear Equationsdiederik

Inexact Newton-type methods for the solution of steady incompressible viscoplastic flows with the SUPG/PSPG finite element formulation

In this work we evaluate the performance of inexact Newton-type schemes to solve the nonlinear equations arising from the SUPG/PSPG finite element formulation of steady viscoplastic incompressible fluid flows. The flow through an abrupt contraction and the rotational flow in eccentric annulus with power law and Bingham rheologies are employed as benchmarks. Our results have shown that inexact s...

Inexact Newton Methods with Restricted Additive Schwarz Based Nonlinear Elimination for Problems with High Local Nonlinearity

The classical inexact Newton algorithm is an efficient and popular technique for solving large sparse nonlinear system of equations. When the nonlinearities in the system are wellbalanced, a near quadratic convergence is often observed, however, if some of the equations are much more nonlinear than the others in the system, the convergence is much slower. The slow convergence (or sometimes dive...