Numerical Evaluation of a Two-Loop Diagram in the Cutoff Regularization

The sunset diagram of λφ4 theory is evaluated numerically in cutoff scheme and a nonzero finite term(in accordance with dimensional regularization (DR) result) is found in contrast to published calculations. This findingdramatically reduces the critical couplings for symmetry breaking in the two-loop effective potential discussed in ourprevious work.     

Well-Posedness by Perturbations of Variational Problems

In this paper, we consider the extension of the notion of well-posedness by perturbations, introduced by Zolezzi for optimization problems, to other related variational problems like inclusion problems and fixed-point problems. Then, we study the conditions under which there is equivalence of the well-posedness in the above sense between different problems. Relations with the so-called diagonal well-posedness are also given. Finally, an application to staircase iteration methods is presented.     

Regularization of Discrete Ill-Posed Problems

The paper concerns conditioning aspects of finite-dimensional problems arising when the Tikhonov regularization is applied to discrete ill-posed problems. A relation between the regularization parameter and the sensitivity of the regularized solution is investigated. The main conclusion is that the condition number can be decreased only to the square root of that for the nonregularized problem. The convergence of solutions of regularized discrete problems to the exact generalized solution is analyzed just in the case when the regularization corresponds to the minimal condition number. The convergence theorem is proved under the assumption of the suitable relation between the discretization level and the data error. As an example the method of truncated singular value decomposition with regularization is considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

On gravitational radiation and the energy flux of matter

A suitable derivative of Einstein's equations in the framework of the teleparallel equivalent of general relativity (TEGR) yields a continuity equation for the gravitational energy‐momentum. In particular, the time derivative of the total gravitational energy is given by the sum of the total fluxes of gravitational and matter fields energy. We carry out a detailed analysis of the continuity equation in the context of Bondi and Vaidya's metrics. In the former space‐time the flux of gravitational energy is given by the well known expression in terms of the square of the news function. It is known that the energy definition in the realm of the TEGR yields the ADM (Arnowitt‐Deser‐Misner) energy for appropriate boundary conditions. Here we show that the same energy definition also describes the Bondi energy. The analysis of the continuity equation in Vaidya's space‐time shows that the variation of the total gravitational energy is determined by the energy flux of matter only.     

Gravitation as Anholonomy

A gravitational field can be seen as the anholonomy of the tetrad fields. This is more explicit in the teleparallel approach, in which the gravitational field-strength is the torsion of the ensuing Weitzenböck connection. In a tetrad frame, that torsion is just the anholonomy of that frame. The infinitely many tetrad fields taking the Lorentz metric into a given Riemannian metric differ by point-dependent Lorentz transformations. Inertial frames constitute a smaller infinity of them, differing by fixed-point Lorentz transformations. Holonomic tetrads take the Lorentz metric into itself, and correspond to Minkowski flat spacetime. An accelerated frame is necessarily anholonomic and sees the electromagnetic field strength with an additional term.     

Steepest Descent, CG, and Iterative Regularization of Ill-Posed Problems

The state of the art iterative method for solving large linear systems is the conjugate gradient (CG) algorithm. Theoretical convergence analysis suggests that CG converges more rapidly than steepest descent. This paper argues that steepest descent may be an attractive alternative to CG when solving linear systems arising from the discretization of ill-posed problems. Specifically, it is shown that, for ill-posed problems, steepest descent has a more stable convergence behavior than CG, which may be explained by the fact that the filter factors for steepest descent behave much less erratically than those for CG. Moreover, it is shown that, with proper preconditioning, the convergence rate of steepest descent is competitive with that of CG.This revised version was published online in October 2005 with corrections to the Cover Date.     

Fourier regularization for a backward heat equation

In this paper a simple and convenient new regularization method for solving backward heat equation—Fourier regularization method is given. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. A numerical example also shows that the method works effectively.     

偏最小二乘回归的贝叶斯正则化神经网络集成模型在证券分析预测中的应用

神经网络集成技术能有效地提高神经网络的预测精度和泛化能力,已经成为机器学习和神经计算领域的一个研究热点.利用Bagging技术和不同的神经网络算法生成集成个体,并用偏最小二乘回归方法从中提取集成因子,再利用贝叶斯正则化神经网络对其集成,以此建立上证指数预测模型.通过上证指数开、收盘价进行实例分析,计算结果表明该方法预测精度高、稳定性好.     

Regularization of singular systems of linear algebraic equations by shifts

Regularization of singular systems of linear algebraic equations by shifts is examined. New equivalent conditions for the shift regularizability of such systems are derived.     

Frozen Landweber Iteration for Nonlinear Ill-Posed Problems

In this paper we propose a modification of the Landweber iteration termed frozen Landweberiteration for nonlinear ill-posed problems.A convergence analysis for this iteration is presented.The numericalperformance of this frozen Landweber iteration for a nonlinear Hammerstein integral equation is compared withthat of the Landweber iteration.We obtain a shorter running time of the frozen Landweber iteration based onthe same convergence accuracy.