A new method for estimating derivatives based on a distribution approach

In many applications, the estimation of derivatives has to be done from noisy measured signal. In this paper, an original method based on a distribution approach is presented. Its interest is to report the derivatives on infinitely differentiable functions. Thus, the estimation of the derivatives is done only from the signal. Besides, this method gives some explicit formulae leading to fast calculus. For all these reasons, it is an efficient method in the case of noisy signals as it will be confirmed in several examples.     

A method for estimating interpolating polynomials

The question of obtaining a lower bound for some interpolating polynomials is considered. Under specific conditions it is proved that these bounds are sharp. As a corollary of the general theorem, under specific restrictions on the points of interpolation, lower bounds for Goncharov interpolation polynomials are obtained which coincide with known upper bounds.Translated from Matematicheskie Zametki, Vol. 17, No. 4, pp. 555–561, April, 1975.     

A method of estimating computational complexity based on input conditions for N-vehicle problem

This paper proposes a method of estimating computational complexity of problem through analyzing its input condition for N-vehicle exploration problem. The N-vehicle problem is firstly formulated to determine the optimal replacement in the set of permutations of 1 to N. The complexity of the problem is factorial of N （input scale of problem）. To balance accuracy and efficiency of general algorithms, this paper mentions a new systematic algorithm design and discusses correspondence between complexity of problem and its input condition, other than just putting forward a uniform approximation algorithm as usual. This is a new technique for analyzing computation of NP problems. The method of corresponding is then presented. We finally carry out a simulation to verify the advantages of the method： 1） to decrease computation in enumeration; 2） to efficiently obtain computational complexity for any N-vehicle case; 3） to guide an algorithm design for any N-vehicle case according to its complexity estimated by the method.     

The threshold method for estimating total rainfall

The threshold method estimates the total rainfall F _G in a region G using the area B _G of the subregion where rainfall intensity exceeds a certain threshold value c. We model the rainfall in a region by a marked spatial point process and derive a correlation formula between F _G and B _G. This correlation depends not only on the rainfall distribution but also on the variation of number of raining sites, showing the importance of taking account of the spatial character of rainfall. In the extreme case where the variation of number of raining sites is dominant, the threshold method may work regardless of rainfall distributions and even regardless of threshold values. We use the lattice gas model from statistical physics to model raining sites and show a huge variation in the number of raining sites is theoretically possible if a phase transition occurs, that is, physically different states coexist. Also, we show by radar observation datasets that there are huge variations of raining sites actually.     

Numerical method for estimating multivariate conditional distributions

Summary  A computational framework for estimation of multivariate conditional distributions is presented. It allows the forecast of the joint distribution of target variables in dependence on explaining variables. The concept can be applied to general distribution families such as stable or hyperbolic distributions. The estimation is based on the numerical minimization of the cross entropy, using the Multi-Level Single-Linkage global optimization method. Nonlinear dependencies of conditional parameters can be modeled with help of general functional approximators such as multi-layer perceptrons. In applications, the information about a complete distribution of forecasts can be used to quantify the reliability of the forecast or for decision support. This is illustrated on a case study concerning the spare parts demand forecast. The improvement of the forecast error due to using non-Gaussian distributions is presented in another case study concerning the truck sales forecast.     

Randomized projection method for estimating angular distributions of polarized radiation based on numerical statistical modeling

To study the intensity of radiation transmitted through a layer of substance, a Monte Carlo algorithm is developed based on the expansion of the corresponding angular distribution density in terms of orthonormalized polynomials with a “Lambert” weight. The algorithm is optimized so as to simplify the computations as much as possible. Even a small effect of polarization and the deviation of the angular distribution from the Lambert one can be estimated rather accurately by applying the algorithm.     

A method for constructing triangular canonical models of commuting operators based on connections with algebraic curves

With the help of points of an algebraic curve we construct prolongations and triangular models of commuting operators in Hilbert space. A canonical triangular model of two arbitrary commuting operators in a finite dimensional space is obtained.     

A two-step method for estimating high-dimensional Gaussian graphical models

The problem of estimating high-dimensional Gaussian graphical models has gained much attention in recent years. Most existing methods can be considered as one-step approaches, being either regression-based or likelihood-based. In this paper, we propose a two-step method for estimating the high-dimensional Gaussian graphical model. Specifically, the first step serves as a screening step, in which many entries of the concentration matrix are identified as zeros and thus removed from further consideration. Then in the second step, we focus on the remaining entries of the concentration matrix and perform selection and estimation for nonzero entries of the concentration matrix. Since the dimension of the parameter space is effectively reduced by the screening step,the estimation accuracy of the estimated concentration matrix can be potentially improved. We show that the proposed method enjoys desirable asymptotic properties. Numerical comparisons of the proposed method with several existing methods indicate that the proposed method works well. We also apply the proposed method to a breast cancer microarray data set and obtain some biologically meaningful results.     

A Levenberg–Marquardt method for estimating polygonal regions

The problem is considered of the estimation of a polygonal region in two dimensions from data approximately marking the outline of the region. A solution is sought by formulating and solving a nonlinear least squares problem. A Levenberg–Marquardt method is developed for this problem, with an implementation which exploits the special structure so that the Levenberg–Marquardt step can be computed efficiently.     

Vibro-acoustic method for estimating a liquid level and viscosity

The goal of this work has been to examine a possibility to measure a liquid level and its viscosity by the vibro-acoustic methods. Preliminary laboratory investigations were completed on a glass vessel filled with solutions of various viscosity and level, excited by a hammer. A microphone and four accelerometers were used as sensors. Few criteria symptoms were checked. For the level and viscosity estimation there were used the placement and values of the Fourier's spectra maximum of the acoustic signal, and of the vibration signals from sensors. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Quadrature method for singular integral equations on closed curves

Summary A method which combines quadrature with trigonometric interpolation is proposed for singular integral equations on closed curves. For the case of the circle, the present method is shown to be equivalent to the trigonometric -collocation method together with numerical quadrature for the compact term, and is shown to be stable inL ² provided the operatorA is invertible inL ². The results are extended to arbitraryC curves, to give a complete error analysis in the scale of Sobolev spacesH ^s . In the final section the case of a non-invertible operatorA is considered.     

A heuristic method for estimating time-series models for forecasting. I

The aim is to develop a heuristic method for estimating time-series models for forecasting. The study consists of two parts. This one presents the analytical framework of the proposed procedure; the second will present the actual algorithm and numerical evaluations of the process. Our approach makes use of the frequency-domain theory of second-order stochastic processes to remedy several of the problems that we encounter in fitting ARIMA-type models for forecasting. Within this framework some of the problems that the present study addresses are: sample size of time series, initial estimates of the coefficients, convergence of difficult data to stable estimates, and computing time.     

A method for estimating criteria weights from intuitionistic preference relations

An intuitionistic preference relation is a powerful means to express decision makers’information of intuitionistic preference over criteria in the process of multi-criteria decision making. In this paper, we first define the concept of its consistence and give the equivalent interval fuzzy preference relation of it. Then we develop a method for estimating criteria weights from it, and then extend the method to accommodate group decision making based on them And finally, we use some numerical examples to illustrate the feasibility and validity of the developed method.     

Pruning of decision alternatives in multiple criteria decision making,based on the Uta method for estimating utilities

A new interactive method for the progressive elimination of elements from a finite set of decision alternatives is proposed. A sequence of alternatives is presented to the decision maker, who places each new alternative presented in rank order relative to the earlier alternatives evaluated. This ranking of elements in a subset of the decision space is used to eliminate other alternatives from further consideration. The approach is broadly based on the UTA method for utility assessment. The emphasis is not, however, on assessing a utility function as such; instead the class of utility functions is used to eliminate elements of the decision space, when the optimality of such elements is inconsistent with the presumed properties of the utility function and the rank orderings given. In this way, the decision maker need only evaluate a relatively small subset of the decision space, before all remaining alternatives are eliminated. The new procedure is illustrated by two numerical examples.     

Newton's method for gradient equations based upon the fixed point map: Convergence and complexity study

Summary An approximate Newton method, based upon the fixed point mapT, is introduced for scalar gradient equations. Although the exact Newton method coincides for such scalar equations with the standard iteration, the structure of the fixed point map provides a way of defining anR-quadratically convergent finite element iteration in the spirit of the Kantorovich theory. The loss of derivatives phenomenon, typically experienced in approximate Newton methods, is thereby avoided. It is found that two grid parameters are sssential,h and . The latter is used to calculate the approximate residual, and is isolated as a fractional step; it is equivalent to the approximation ofT. The former is used to calculate the Newton increment, and this is equivalent to the approximation ofT. The complexity of the finite element computation for the Newton increment is shown to be of optimal order, via the Vitukin inequality relating metric entropy andn-widths.Research supported by National Science Foundation grant DMS-8721742     

计算微分代数系统稳定域的迭代Lyapunov函数方法

用迭代Lyapunov函数方法对微分代数系统稳定域进行了研究,根据所研究的微分代数系统形式,构造一个Lyapunov函数,然后对这个Lyapunov函数进行逐次迭代,给出了微分代数系统稳定域逐次扩大的迭代算法,数值实验表明迭代Lyapunov函数方法应用于微分代数系统稳定域的估计比单个Lyapunov函数具有良好的优越性。     

On the accelerated iterative method for estimating the optimum overrelaxation parameter

This paper is concerned with the iterative method for estimating the optimum overrelaxation parameter. The improved power method (IP method) with the greatest rate of convergence is derived and compared with the Chebyshev polynomial iterative method (CP method) and the other iterative methods. Two algorithms (algorithms A and B) based on the IP method are presented. Some numerical results are shown.     

A semiparametric method for estimating nonlinear autoregressive model with dependent errors

The first-order nonlinear autoregressive model is considered and a semiparametric method is proposed to estimate regression function. In the presented model, dependent errors are defined as first-order autoregressive AR(1). The conditional least squares method is used for parametric estimation and the nonparametric kernel approach is applied to estimate regression adjustment. In this case, some asymptotic behaviors and simulated results for the semiparametric method are presented. Furthermore, the method is applied for the financial data in Iran’s Tejarat-Bank.     

Frequency-domain regression method for estimating CTF models of building multilayer constructions

The conduction transfer function (CTF) models of heat conduction through building constructions are widely used in building energy analysis and heating, ventilation, and air conditioning (HVAC) system design and simulation. A frequency-domain regression (FDR) method is developed to estimate the CTF model of a building construction from its theoretical response characteristics in this paper. First, the theoretical response characteristics are calculated simply by numerical matrix multiplication. The CTF coefficients are then obtained by simply solving a set of linear equations. The tests and comparisons have shown that CTF models obtained by the FDR method are completely equivalent to those found by the methods currently available. The FDR method can provide a short series of CTF coefficients, and the models by this method have a high accuracy in calculating heat gain/loss through building constructions. The FDR method is very simple and straightforward, has high computational speeds, and needs less computational efforts. Therefore, the FDR method is much easier and convenient to use and implement in building energy analysis and HVAC system simulation programs.