A variable V-cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented. An analysis under a mild regularity assumption shows that the preconditioner is uniform. The interior penalty method is then combined with a discontinuous Galerkin scheme to arrive at a discretization scheme for an advection-diffusion problem, for which an error estimate i...

In this paper, we study the Nyström type subsampling for large scale kernel methods to reduce the computational complexities of big data. We discuss the multi-penalty regularization scheme based on Nyström type subsampling which is motivated from well-studied manifold regularization schemes. We develop a theoretical analysis of multi-penalty least-square regularization scheme under the general ...

We introduce a mean field game with rank-based reward: competing agents optimize their effort to achieve a goal, are ranked according to their completion time, and paid a reward based on their relative rank. First, we propose a tractable Poissonian model in which we can describe the optimal effort for a given reward scheme. Second, we study the principal–agent problem of designing an optimal re...

Although local governments have issued relevant reward and penalty policies, there are still problems of medical waste disposal in China, particularly light the special situation COVID-19 pandemic. Furthermore, these generated game between enterprises. Accordingly, based on evolutionary theory, this paper establishes analyzes system enterprises under four modes: static penalty, dynamic penalty....

In this paper, we considered the role of penalty when the higher-order conjugate gradient method (HCGM) was used as a computational scheme for the minimization of penalised cost functions for optimal control problems described by linear systems and integral quadratic costs. For this family of commonly encountered problems, we find out that the conventional penalty methods require very large pen...

In learning theory, the convergence issues of the regression problem are investigated with the least square Tikhonov regularization schemes in both the RKHS-norm and the L -norm. We consider the multi-penalized least square regularization scheme under the general source condition with the polynomial decay of the eigenvalues of the integral operator. One of the motivation for this work is to dis...

A vertex-based finite volume method for Laplace operator on triangular grids is proposed in which Dirichlet boundary conditions are implemented weakly. The scheme satisfies a summation-by-parts (SBP) property including boundary conditions which can be used to prove energy stability of the scheme for the heat equation. A Nitsche-type penalty term is proposed which gives improved accuracy. The sc...

How do reward outcomes affect early visual performance? Previous studies found a suboptimal influence, but they ignored the non-linearity in how subjects perceived the reward outcomes. In contrast, we find that when the non-linearity is accounted for, humans behave optimally and maximize expected reward. Our subjects were asked to detect the presence of a familiar target object in a cluttered s...

We present a novel approach to the modeling of motor responses based on statistical decision theory. We begin with the hypothesis that subjects are ideal motion planners who choose movement trajectories to minimize expected loss. We derive predictions of the hypothesis for movement in environments where contact with specified regions carries rewards or penalties. The model predicts shifts in a ...