Approximation of Generalized Biaxisymmetric Potentials in $L^{\beta}$-norm

On the Generalized Matrix Approximation Problems in the Spectral Norm

In this paper theoretical results regarding a generalized minimum rank matrix approximation problem in the spectral norm are presented. An alternative solution expression for the generalized matrix approximation problem is obtained. This alternative expression provides a simple characterization of the achievable minimum rank, which is shown to be the same as the optimal objective value of the c...

Parsimonious Least Norm Approximation

A theoretically justiiable fast nite successive linear approximation algorithm is proposed for obtaining a parsimonious solution to a corrupted linear system Ax = b + p, where the corruption p is due to noise or error in measurement. The proposed linear-programming-based algorithm nds a solution x by parametrically minimizing the number of nonzero elements in x and the error k Ax ? b ? p k 1. N...

All-Norm Approximation Algorithms

A major drawback in optimization problems and in particular in scheduling problems is that for every measure there may be a different optimal solution. In many cases the various measures are different lp norms. We address this problem by introducing the concept of an All-norm ρ-approximation algorithm, which supplies one solution that guarantees ρ-approximation to all lp norms simultaneously. S...

Generalized Order and Best Approximation of Entire Function in Lp-Norm

A choice of norm in discrete approximation ∗

We consider the problem of choice of norms in discrete approximation. First, we describe properties of the standard l1, l2 and l∞ norms, and their essential characteristics for using as error criteria in discrete approximation. After that, we mention the possibility of applications of the so-called total least squares and total least lp norm, for finding the best approximation. Finally, we take...