These notes have a dual goal. On the one hand we shall give an overview of the recently introduced class of scalable frames. These are (finite) frames with the property that each frame vector can be rescaled in such a way that the resulting frames are tight. This process can be viewed as a preconditioning method for finite frames. In particular, we shall: (1) describe the class of scalable fram...

Several problems in early vision have been formulated in the past in a regularization framework. These problems when discretized lead to large sparse linear systems. In this paper, we present a novel physically-based adaptive preconditioning technique which can be used in conjunction with a conjugate gradient algorithm to drastically improve the speed of convergence for solving the aforemention...

Preconditioning is the most common approach for accelerating an iterative method and consists in solving an auxilliary problem structurally close to the original one. In most situations, the art of preconditioning consists in building in a efficient way a matrix or a sequence of matrices. This explicit approach is not however always possible and there are situations in which preconditioned vers...

Two types of acceleration techniques, H-matrix arithmetics and an H-matrix-based variable preconditioning (VP), as well their combination are applied to a linear-system solver in the shielding current analysis cracked high-temperature superconducting film. Although seems be most effective three results computations show that, from standpoint performance, neither VP nor is superior arithmetics. ...

When solving a linear system in parallel, a large overhead in using an incomplete LU factorization as a preconditioner may annihilate any gains made from the improved convergence. This overhead is due to the inherently sequential nature of such a preconditioning. Multicoloring of the subdomains assigned to processors is a common remedy for increasing the parallelism of a global ordering. Howeve...

When one approximates elliptic equations by the spectral collocation method on the Chebyshev-Gauss-Lobatto (CGL) grid, the resulting coefficient matrix is dense and illconditioned. It is known that a good preconditioner, in the sense that the preconditioned system becomes well conditioned, can be constructed with finite difference on the CGL grid. However, there is a lack of an efficient solver...

Multilevel techniques are very effective tools for preconditioning iterative Krylov methods in the solution of sparse linear systems; among them, Algebraic MultiGrid (AMG) are widely employed variants. In [2, 4] it is shown how parallel smoothed aggregation techniques can be used in combination with domain decomposition Schwarz preconditioners to obtain AMG preconditioners; the effectiveness of...

Abstract: In this paper, constraint rotation techniques are considered for preconditioning 0–1 knapsack problems. These techniques permit one to generate new inequalities by means of rotation of the original ones in order to approach the convex hull associated with the feasible integer points. The time and space complexities of Kianfar’s inequality rotation algorithm for combinatorial problems ...

The reduced basis methodology is an efficient approach to solve parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step utilizes this approximation, the reduced basis, to solve a smaller reduced problem, which provides an accurate estimate of the solution. Traditionally, the re...