Abstract. In this paper, we develop a concrete algorithm for phase retrieval, which we refer to as GaussNewton algorithm. In short, this algorithm starts with a good initial estimation, which is obtained by a modified spectral method, and then update the iteration point by a Gauss-Newton iteration step. We prove that a re-sampled version of this algorithm quadratically converges to the solution...

The problem of determining minimum-fuel maneuver sequences for a four-spacecraft formation is considered. The objective of this paper is to determine fuel-optimal configuration trajectories that transfer a four spacecraft formation from an initial parking orbit to a desired terminal reference orbit while satisfying particular formation constraints. In this paper, the configuration problem is so...

We investigate the application of multigrid techniques to the solution of the \classic" radiosity equation. After overviews of the global illumination problem and of radiosity, we describe the latter's solution via multigrid methods. An implementation of the multigrid algorithm presented here is able to solve the classic radiosity equation in about 50% of the time required by the more commonly-...

The notions of Lipschitz conditions with L average are introduced to the study of convergence analysis of Gauss-Newton’s method for singular systems of equations. Unified convergence criteria ensuring the convergence of Gauss-Newton’s method for one kind of singular systems of equations with constant rank derivatives are established and unified estimates of radii of convergence balls are also o...

K e y w o r d s G a u s s N e w t o n ' s method, Lipschitz conditions with L average, Convergence ball, Uniqueness bali. 1. I N T R O D U C T I O N Finding the solution of a nonlinear operator equation f(x) = 0 (1.1) in Banach space X is a very general subject which is widely used in both theoretical and applied areas of mathematics, where f is a nonlinear operator from some domain D in a real...

The Kaczmarz and Gauss-Seidel methods both solve a linear system Xβ = y by iteratively refining the solution estimate. Recent interest in these methods has been sparked by a proof of Strohmer and Vershynin which shows the randomized Kaczmarz method converges linearly in expectation to the solution. Lewis and Leventhal then proved a similar result for the randomized Gauss-Seidel algorithm. Howev...

Classical iterative methods for the solution of algebraic linear systems of equations proceed by solving at each step a simpler system of equations. When this system is itself solved by an (inner) iterative method, the global method is called a two-stage iterative method. If this process is repeated, then the resulting method is called a nested iterative method. We study the convergence of such...