Abstract — We show in this paper that many different least-squares problems which have applications in signal processing may be seen as special cases of a more general vector space minimization problem called the Minimum Norm problem. We show that special cases of the Minimum Norm problem include: least squares fitting of a finite set of points to a linear equation and to a quadratic equation; ...

We study the effect of a general singular perturbation on a nonconvex variational problem with infinitely many solutions. Using a scaling argument and the theory of T-convergence of nonlinear functionals, we show that if the solutions of the perturbed problem converge in L1 as the perturbation parameter goes to zero, then the limit function satisfies a classical minimal surface problem. Introdu...

We report on computational experience with an implementation of three algorithms for the general economic equilibrium problem. As a result we get that the projection algorithm for variational inequalities increases the size of solvable models by a factor of 5-10 in comparison with the classical homotopy method. As a third approach we implemented a simulated annealing heuristic which might be su...

The tractability of multivariate problems has usually been studied only for the approximation of linear operators. In this paper we study the tractability of quasilinear multivariate problems. That is, we wish to approximate nonlinear operators Sd(·, ·) that depend linearly on the first argument and satisfy a Lipschitz condition with respect to both arguments. Here, both arguments are functions...

and Applied Analysis 3 Proof. First, we show that {x n } is bounded. In fact, let z ∈ Ω. Since {λ n,i } ⊂ (0, 2/‖A‖ 2 ), the operators P Ci (I − λ n,i A ∗ (I − P Qi )A) are nonexpansive, and hence we have 󵄩󵄩󵄩󵄩xn+1 − z 󵄩󵄩󵄩󵄩 = 󵄩󵄩󵄩󵄩󵄩󵄩󵄩󵄩󵄩 α n x n + β n f (x n )

Alcohol-related health problems place a significant burden on general hospitals. Statistics indicate that one in seven acute hospital admissions is a result of alcohol misuse and that one in six attendances at A&E is alcohol related, rising to eight out of 10 at peak times on weekend evenings. Nurses have a role to play in estimating a patient's alcohol use and, if appropriate, providing 'brief...

In this article, we propose and analyze a computational method for numerical solution of general two point boundary value problems. Method is tested on problems to ensure the computational eciency. We have compared numerical results with results obtained by other method in literature. We conclude that propose method is computationally ecient and eective.