In this paper we analyse applicability and robustness of Markov chain Monte Carlo algorithms for eigenvalue problems. We restrict our consideration to real symmetric matrices.
Almost Optimal Monte Carlo (MAO) algorithms for solving eigenvalue problems are formulated. Results for the structure of both – systematic and probability error are presented. It is shown that the values of both errors can be controlled independently by different algorithmic parameters. The results present how the systematic error depends on the matrix spectrum. The analysis of the probability error is presented. It shows that the close (in some sense) the matrix under consideration is to the stochastic matrix the smaller is this error. Sufficient conditions for constructing robust and interpolation Monte Carlo algorithms are obtained. For stochastic matrices an interpolation Monte Carlo algorithm is constructed.
A number of numerical tests for large symmetric dense matrices are performed in order to study experimentally the dependence of the systematic error from the structure of matrix spectrum. We also study how the probability error depends on the balancing of the matrix. 相似文献
This paper presents a statistical method for comparison of two groups of real-valued data, based on nonparametric predictive inference (NPI), with the tails of the data possibly terminated, leading to small values being left-censored and large values being right-censored. Such tails termination can occur due to several reasons, including limits of detection, consideration of outliers, and specific designs of experiments. NPI is a statistical approach based on few assumptions, with inferences strongly based on data and with uncertainty quantified via lower and upper probabilities. We present NPI lower and upper probabilities for the event that the value of a future observation from one group is less than the value of a future observation from the other group, and we discuss several special cases that relate to well-known statistical problems. 相似文献
It is well known that the robust counterpart introduced by Ben-Tal and Nemirovski (Math Oper Res 23:769–805, 1998) increases
the numerical complexity of the solution compared to the original problem. Kočvara, Nemirovski and Zowe therefore introduced
in Kočvara et al. (Comput Struct 76:431–442, 2000) an approximation algorithm for the special case of robust material optimization,
called cascading. As the title already indicates, we will show that their method can be seen as an adjustment of standard exchange methods
to semi-infinite conic programming. We will see that the adjustment can be motivated by a suitable reformulation of the robust
conic problem.
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This paper revisits some asymptotic properties of the robust nonparametric estimators of order-m and order-α quantile frontiers and proposes isotonized version of these estimators. Previous convergence properties of the order-m frontier are extended (from weak uniform convergence to complete uniform convergence). Complete uniform convergence of the order-m (and of the quantile order-α) nonparametric estimators to the boundary is also established, for an appropriate choice of m (and of α, respectively) as a function of the sample size. The new isotonized estimators share the asymptotic properties of the original ones and a simulated example shows, as expected, that these new versions are even more robust than the original estimators. The procedure is also illustrated through a real data set. 相似文献
In this paper, we consider a one-dimensional dam-river system, described by a diffusive-wave equation and often used in hydraulic
engineering to model the dynamic behavior of the unsteady flow in a river for shallow water when the flow variations are not
important. We propose an integral boundary control which leads to a nondissipative closed-loop system with noncollocated actuators
and sensors; hence, two main difficulties arise: first, how to show the C0-semigroup generation and second, how to achieve the stability of the system. To overcome this situation, the Riesz basis
methodology is adopted to show that the closed-loop system generates an analytic semigroup. Concerning the stability, the
shooting method is applied to assign the spectrum of the system in the open left-half plane and ensure its exponential stability
as well as the output regulation. Numerical simulations are presented for a family of system parameters.
The authors express their sincere thanks to Boumenir Amin for valuable comments and suggestions. The first author acknowledges
the support of Sultan Qaboos University. The second author was supported by the National Natural Science Foundation of China. 相似文献
During metamodel-based optimization three types of implicit errors are typically made. The first error is the simulation-model error, which is defined by the difference between reality and the computer model. The second error is the metamodel error, which is defined by the difference between the computer model and the metamodel. The third is the implementation error. This paper presents new ideas on how to cope with these errors during optimization, in such a way that the final solution is robust with respect to these errors. We apply the robust counterpart theory of Ben-Tal and Nemirovsky to the most frequently used metamodels: linear regression and Kriging models. The methods proposed are applied to the design of two parts of the TV tube. The simulation-model errors receive little attention in the literature, while in practice these errors may have a significant impact due to propagation of such errors. 相似文献
We obtain a computable a posteriori error bound on the broken energy norm of the error in the Fortin-Soulie finite element approximation of a linear second order elliptic problem with variable permeability. This bound is shown to be efficient in the sense that it also provides a lower bound for the broken energy norm of the error up to a constant and higher order data oscillation terms. The estimator is completely free of unknown constants and provides a guaranteed numerical bound on the error.
To deal with the robust portfolio selection problem where only partial information on the exit time distribution and on the conditional distribution of portfolio return is available, we extend the worst-case VaR approach and formulate the corresponding problems as semi-definite programs. Moreover, we present some numerical results with real market data. 相似文献
In this note we address the problem of finding the GM-estimator for the location parameter of a univariate random variable. When this problem is non-convex but d.c. one can use a standard covering method, which, in the one-dimensional case has a simple form. In this paper we exploit the structure of the problem in order to obtain d.c. decompositions with certain optimality properties in the application of the algorithm. Numerical results show that this general-purpose algorithm outperforms previous ad-hoc methods for this problem. 相似文献