An Arnoldi-Type Algorithm for Parametric Finite Element Modelling of Microwave Components

In this paper, we present an efficient model order reduction (MOR) technique for computing the solution of a linear equation system depending on a multivariate polynomial of scalar parameters. We propose a moment-matching projection method based on the concept of multivariate Krylov spaces of higher order. The new method exhibits greater stability and allows to build models of higher order than previous approaches. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A new test for multivariate normality

We propose a new class of rotation invariant and consistent goodness-of-fit tests for multivariate distributions based on Euclidean distance between sample elements. The proposed test applies to any multivariate distribution with finite second moments. In this article we apply the new method for testing multivariate normality when parameters are estimated. The resulting test is affine invariant and consistent against all fixed alternatives. A comparative Monte Carlo study suggests that our test is a powerful competitor to existing tests, and is very sensitive against heavy tailed alternatives.     

Wildland fire growth prediction method based on Multiple Overlapping Solution

Several Data-Driven Methods have been developed to try to solve the input parameters uncertainty when considering problems like Wildfires Prediction. In general, these methods operate over a large number of input parameters, and consider the most recent known behavior of wildfires. The purpose of the methods is to find the parameter set that best describes the real situation under consideration. Therefore, it is presumed that the same set of values could be used to predict the immediate future.However, because this kind of prediction is based on a single set of parameters, for those parameters that present a dynamic behavior (e.g. wind direction and speed), the new optimized values are not adequate to make a prediction.In this paper we propose an alternative method developed in a new branch of Data-Driven Prediction, which we called Multiple Overlapping Solution. This method combines statistical concepts and HPC (High Performance Computing) to obtain a higher quality prediction.     

Deformable orthogonal grids: lemniscates

In this paper we describe a technique, based on complex polynomials, for creating plane regions with a hole and propose a new method to produce an orthogonal grid on it. The thickness of the grid can be easily controlled and the sizes of the cells can be automatically estimated. The grid is automatically adapted to the boundary of the region. We offer parameters for the control of the geometric shape of the region, which depend on the roots of the polynomial and its derivative.     

THE TWO-LEVEL STABILIZED FINITE ELEMENT METHOD BASED ON MULTISCALE ENRICHMENT FOR THE STOKES EIGENVALUE PROBLEM

In this paper,we first propose a new stabilized finite element method for the Stokes eigenvalue problem.This new method is based on multiscale enrichment,and is derived from the Stokes eigenvalue problem itself.The convergence of this new stabilized method is proved and the optimal priori error estimates for the eigenfunctions and eigenvalues are also obtained.Moreover,we combine this new stabilized finite element method with the two-level method to give a new two-level stabilized finite element method for the Stokes eigenvalue problem.Furthermore,we have proved a priori error estimates for this new two-level stabilized method.Finally,numerical examples confirm our theoretical analysis and validate the high effectiveness of the new methods.     

A Cross-Entropy Approach to the Estimation of Generalized Linear Multilevel Models

In this article, we use the cross-entropy method for noisy optimization for fitting generalized linear multilevel models through maximum likelihood. We propose specifications of the instrumental distributions for positive and bounded parameters that improve the computational performance. We also introduce a new stopping criterion, which has the advantage of being problem-independent. In a second step we find, by means of extensive Monte Carlo experiments, the most suitable values of the input parameters of the algorithm. Finally, we compare the method to the benchmark estimation technique based on numerical integration. The cross-entropy approach turns out to be preferable from both the statistical and the computational point of view. In the last part of the article, the method is used to model the probability of firm exits in the healthcare industry in Italy. Supplemental materials are available online.     

Using Experimental Design to Find Effective Parameter Settings for Heuristics

In this paper, we propose a procedure, based on statistical design of experiments and gradient descent, that finds effective settings for parameters found in heuristics. We develop our procedure using four experiments. We use our procedure and a small subset of problems to find parameter settings for two new vehicle routing heuristics. We then set the parameters of each heuristic and solve 19 capacity-constrained and 15 capacity-constrained and route-length-constrained vehicle routing problems ranging in size from 50 to 483 customers. We conclude that our procedure is an effective method that deserves serious consideration by both researchers and operations research practitioners.     

A new decision support model in multi-criteria decision making with intuitionistic fuzzy sets based on risk preferences and criteria reduction

In this paper, we propose a new model for decision support to address the ‘large decision table’ (eg, many criteria) challenge in intuitionistic fuzzy sets (IFSs) multi-criteria decision-making (MCDM) problems. This new model involves risk preferences of decision makers (DMs) based on the prospect theory and criteria reduction. First, we build three relationship models based on different types of DMs’ risk preferences. By building different discernibility matrices according to relationship models, we find useful criteria for IFS MCDM problems. Second, we propose a technique to obtain weights through discernibility matrix. Third, we also propose a new method to rank and select the most desirable choice(s) according to weighted combinatorial advantage values of alternatives. Finally, we use a realistic voting example to demonstrate the practicality and effectiveness of the proposed method and construct a new decision support model for IFS MCDM problems.     

Empirical likelihood for median regression model with designed censoring variables

We propose a new and simple estimating equation for the parameters in median regression models with designed censoring variables, and then apply the empirical log likelihood ratio statistic to construct confidence region for the parameters. The empirical log likelihood ratio statistic is shown to have a standard chi-square distribution, which makes this method easy to implement. At the same time, another empirical log likelihood ratio statistic is proposed based on an existing estimating equation and the limiting distribution of the empirical likelihood ratio statistic is shown to be a sum of weighted chi-square distributions. We compare the performance of the empirical likelihood confidence region based on the new estimating equation, with that based on the existing estimating equation and a normal approximation method by simulation studies.     

Cross approximation in tensor electron density computations

We propose new tensor approximation algorithms for certain discrete functions related with Hartree–Fock/Kohn–Sham equations. Given a canonical tensor representation for the electron density function (for example, produced by quantum chemistry packages such as MOLPRO), we obtain its Tucker approximation with much fewer parameters than the input data and the Tucker approximation for the cubic root of this function, which is part of the Kohn–Sham exchange operator. The key idea is in the fast and accurate prefiltering of possibly large‐scale factors of the canonical tensor input. The new algorithms are based on the incomplete cross approximation method applied to matrices and tensors of order 3 and outperform other tools for the same purpose. First, we show that the cross approximation method is robust and much faster than the singular value decomposition‐based approach. As a consequence, it becomes possible to increase the resolution of grid and the complexity of molecules that can be handled by the Hartree–Fock chemical models. Second, we propose a new fast approximation method for f^1/3(x, y, z), based on the factor prefiltering method for f(x, y, z) and certain mimic approximation hypothesis. Third, we conclude that the Tucker format has advantages in the storage and computation time compared with the ubiquitous canonical format. Copyright © 2009 John Wiley & Sons, Ltd.     

一般变分不等式的一个新的下降投影算法

本文运用辅助问题原理,给出一般变分不等式一个新的投影下降算法,并证明在伪单调条件下,算法是收敛的.     

Solving the multiobjective possibilistic linear programming problem

In conventional multiobjective decision making problems, the estimation of the parameters of the model is often a problematic task. Normally they are either given by the decision maker (DM), who has imprecise information and/or expresses his considerations subjectively, or by statistical inference from past data and their stability is doubtful. Therefore, it is reasonable to construct a model reflecting imprecise data or ambiguity in terms of fuzzy sets for which a lot of fuzzy approaches to multiobjective programming have been developed. In this paper we propose a method to solve a multiobjective linear programming problem involving fuzzy parameters (FP-MOLP), whose possibility distributions are given by fuzzy numbers, estimated from the information provided by the DM. As the parameters, intervening in the model, are fuzzy the solutions will be also fuzzy. We propose a new Pareto Optimal Solution concept for fuzzy multiobjective programming problems. It is based on the extension principle and the joint possibility distribution of the fuzzy parameters of the problem. The method relies on α-cuts of the fuzzy solution to generate its possibility distributions. These ideas are illustrated with a numerical example.     

Convergence of a non-interior smoothing method for variational inequality problems

The variational inequality problem can be reformulated as a system of equations. One can solve the reformulated equations to obtain a solution of the original problem. In this paper, based on a symmetric perturbed min function, we propose a new smoothing function, which has some nice properties. By which we propose a new non-interior smoothing algorithm for solving the variational inequality problem, which is based on both the non-interior continuation method and the smoothing Newton method. The proposed algorithm only needs to solve at most one system of equations at each iteration. In particular, we show that the algorithm is globally linearly and locally quadratically convergent under suitable assumptions. The preliminary numerical results are reported.     

Relation between total variation and persistence distance and its application in signal processing

In this paper we establish the new notion of persistence distance for discrete signals and study its main properties. The idea of persistence distance is based on recent developments in topological persistence for assessment and simplification of topological features of data sets. Particularly, we establish a close relationship between persistence distance and discrete total variation for finite signals. This relationship allows us to propose a new adaptive denoising method based on persistence that can also be regarded as a nonlinear weighted ROF model. Numerical experiments illustrate the ability of the new persistence based denoising method to preserve significant extrema of the original signal.     

非线性互补问题非精确逐次逼近法的全局收敛性

本文针对非线性互补问题,提出了与其等价的非光滑方程的非精确逐次逼近算法,并在一定条件下证明了该算法的全局收敛性。     

Reliability analysis of the metal forming process

In this paper, we propose a reliability–mechanical study combination for treating the metal forming process. This combination is based on the augmented Lagrangian method for solving the deterministic case and the response surface method. Our goal is the computation of the failure probability of the frictionless contact problem. Normally, contact problems in mechanics are particularly complex and have to be solved numerically. There are several numerical techniques available for computing the solution. However, some design parameters are uncertain and the deterministic solutions could be unacceptable. Thus, a mechanical contact study is an important subject for reliability analysis: the augmented Lagrangian method coupled with the first order reliability method, and we use the Monte Carlo method to obtain the founding results. The metal forming process is treated numerically to validate the new approach.     

A strategy for choosing Gegenbauer reconstruction parameters for numerical stability

The Gegenbauer reconstruction method was first proposed in 1992, but in early studies no attempts were made to optimize the relevant parameters of this method. These parameters were allowed to grow proportionally with the number of nodes which, in many cases, resulted in exponential convergence for a selected range of the proportionality constants. Early studies also made clear that very large error bounds could be expected if these key parameters were not chosen carefully. Subsequent studies then pointed out that, although unrelated to the method’s analytically predictable domains of poor accuracy, round-off errors could also sabotage the method’s accuracy. The challenge of successfully implementing a Gegenbauer reconstruction then rests on understanding the performance trade-offs we can expect when choosing the key parameters in accordance with different objectives.In this study, we propose a new strategy for choosing optimal parameters in the Chebyshev-Gegenbauer reconstruction method, specifically to achieve numerical stability. This strategy is based on asymptotic analysis as well as minimization problems in one and two dimensions. The effectiveness of our approach, which could also be applied to a wider selection of polynomials is then illustrated with results from numerical experiments.     

COMPUTATIONAL MULTISCALE METHODS FOR LINEAR HETEROGENEOUS POROELASTICITY

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling.This poroelasticity problem suffers from rapidly oscillating material parameters,which calls for a thorough numerical treatment.In this paper,we propose a method based on the local orthogonal decomposition technique and motivated by a similar approach used for linear thermoelasticity.Therein,local corrector problems are constructed in line with the static equations,whereas we propose to consider the full system.This allows to benefit from the given saddle point structure and results in two decoupled corrector problems for the displacement and the pressure.We prove the optimal first-order convergence of this method and verify the result by numerical experiments.     

一种新的迭代收敛阶数的证明与推广

迭代方法是求解非线性方程近似根的重要方法.本文基于隐函数存在定理,提出了一种新的迭代方法收敛性和收敛阶数的证明方法,并分别对牛顿(Newton)和柯西(Cauchy)迭代方法迭代收敛性和收敛阶数进行了证明.最后,利用本文提出的证明方法,证明了基于三次泰勒(Taylor)展式构成的迭代格式是收敛的,收敛阶数至少为4,并提出猜想,基于n次泰勒展式构成的迭代格式是收敛的,收敛阶数至少为(n+1).     

基于k-means和邻域粗糙集的航空客户价值分类研究

对客户价值进行分类, 识别重要价值客户, 对航空公司获利至关重要。本文提出了基于k-means和邻域粗糙集的航空客户价值分类模型。首先, 从客户的当前价值和潜在价值双视角出发, 建立了航空客户综合价值评价指标体系; 之后, 采用基于Elbow的k-means方法对航空客户进行聚类, 采用邻域粗糙集方法对决策系统进行指标约简, 根据约简后的决策系统完成客户价值初筛。评估前先使用SMOTE方法消除数据的不平衡性, 而后采用网格搜索组合分类器的方法对航空客户价值分类的效果进行评估和检验。最后, 根据评估结果对航空客户价值细分。文末, 对国内某航空公司的62988条真实客户记录进行了实证分析和验证, 其中, 潜在VIP客户群的分类准确率达到了92%, 从而为航空客户价值分类提供了一种新思路。