In this report we present computational methods for the best multilinear rank approximation problem. We consider algorithms build on quasi-Newton methods operating on product of Grassmann manifolds. Specifically we test and compare methods based on BFGS and L-BFGS updates in local and global coordinates with the Newton-Grassmann and alternating least squares methods. The performance of the quas...

This paper describes a fall-back procedure for use with the Gauss-Newton method for nonlinear least-squares problems. While the basic Gauss-Newton algorithm is often successful, it is well-known that it can sometimes generate poor search directions and exhibit slow convergence. For dealing with such situations we suggest a new two-dimensional search strategy. Numerical experiments indicate that...

Second order methods for optimization call for the solution of sequences of linear systems. In this survey we will discuss several issues related to the preconditioning of such sequences. Covered topics include both techniques for building updates of factorized preconditioners and quasi-Newton approaches. Sequences of unsymmetric linear systems arising in NewtonKrylov methods will be considered...

This paper deals with the solution of large linear systems which arise when certain optimization methods are applied in image de-blurring. An unconstrained penalized least squares minimization problem with total variation penalty is considered. Also addressed are several penalized least squares problems with nonnegativity constraints imposed on the solution. In each case, quasi-Newton technique...

soil conservation service (scs) adjusted the kostiakovs infiltration model by adding a constant coefficient, for improvement of estimation. the improved model has three constant parameters, which are difficult to calculate. so scs has taken the third constant parameter as equal to 0.65-0.7 cm to simplify the estimation. this parameter varies in different soil and often outranges the scs estimat...

The alternating direction method of multipliers (ADMM) is applied to a constrained linear least-squares problem, where the objective function is a sum of two least-squares terms and there are box constraints. The original problem is decomposed into two easier least-squares subproblems at each iteration, and to speed up the inner iteration we linearize the relevant subproblem whenever it has no ...

In this article we present a new method for seismic image restoration. When observed, a seismic image is the result of an initial deposit system that has been transformed by a set of successive geological deformations (flexures, fault slip, etc) that occurred over a large period of time. The goal of seismic restoration consists in inverting the deformations to provide a resulting image that dep...