Iterative reconstruction methods for wave equations

Iterative Reconstruction Methods for Non-cartesian Mri

For magnetic resonance imaging (MRI) with Cartesian k-space sampling, a simple inverse FFT usually suffices for image reconstruction. More sophisticated image reconstruction methods are needed for non-Cartesian k-space acquisitions. Regularized least-squares methods for image reconstruction involve minimizing a cost function consisting of a least-squares data fit term plus a regularizing roughn...

Iterative Methods for Linear and Nonlinear Equations

Iterative Methods for Nonlinear Elliptic Equations

‖f(u)− f(v)‖−1 ≤ L‖u− v‖−1. We drop the dependence of f on x to emphasis the nonlinearity in u. Let Vh ⊂ H 0 (Ω) be the linear finite element space associated to a quasi-uniform mesh Th. The nonlinear Garlerkin method is: find uh ∈ Vh such that (2) Auh = f(uh) in Vh, where A : H 0 (Ω)→ H−1(Ω) is the elliptic operator defined by −∆. We shall assume the existence and locally uniqueness of the sol...

On Preconditioned Iterative Methods for Burgers Equations

We study the Newton method and a fixed-point method for solving the system of nonlinear equations arising from the Sinc-Galerkin discretization of the Burgers equations. In each step of the Newton method or the fixedpoint method, a structured subsystem of linear equations is obtained and needs to be solved numerically. In this paper, preconditioning techniques are applied to solve such linear s...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence