Kind Of Projection Method Research Articles

Projection methods for stochastic differential equations with conserved quantities

In this paper, we consider the numerical methods preserving single or multiple conserved quantities, and these methods are able to reach high order of strong convergence simultaneously based on some kinds of projection methods. The mean-square convergence orders of these methods under certain conditions are given, which can reach order 1.5 or even 2 according to the supporting methods embedded in the projection step. Finally, three numerical experiments are taken into account to show the superiority of the projection methods.

Stable and accurate pressure approximation for unsteady incompressible viscous flow

How to properly specify boundary conditions for pressure is a longstanding problem for the incompressible Navier-Stokes equations with no-slip boundary conditions. An analytical resolution of this issue stems from a recently developed formula for the pressure in terms of the commutator of the Laplacian and Leray projection operators. Here we make use of this formula to (a) improve the accuracy of computing pressure in two kinds of existing time-discrete projection methods implicit in viscosity only, and (b) devise new higher-order accurate time-discrete projection methods that extend a slip-correction idea behind the well-known finite-difference scheme of Kim and Moin. We test these schemes for stability and accuracy using various combinations of C^0 finite elements. For all three kinds of time discretization, one can obtain third-order accuracy for both pressure and velocity without a time-step stability restriction of diffusive type. Furthermore, two kinds of projection methods are found stable using piecewise-linear elements for both velocity and pressure.

Subspace methods for face recognition

Studying the inherently high-dimensional nature of the data in a lower dimensional manifold has become common in recent years. This is generally known as dimensionality reduction. A very interesting strategy for dimensionality reduction is what is known as subspace analysis. Beginning with the Eigenface method, face recognition and in general computer vision has witnessed a growing interest in algorithms that capitalize on this idea and an ample number of such efficient algorithms have been proposed. These algorithms mainly differ in the kind of projection method used (linear or non-linear) or in the criterion employed for classification. The objective of this paper is to provide a comprehensive performance evaluation of about twenty five different subspace algorithms under several important real time test conditions. For this purpose, we have considered the performance of these algorithms on data taken from four standard face and object databases namely ORL, Yale, FERET and the COIL-20 object database. This paper also presents some theoretical aspects of the algorithm and the analysis of the simulations carried out.

Eigenspace-Based Face Recognition: A Comparative Study of Different Approaches

Eigenspace-based face recognition corresponds to one of the most successful methodologies for the computational recognition of faces in digital images. Starting with the Eigenface-Algorithm, different eigenspace-based approaches for the recognition of faces have been proposed. They differ mostly in the kind of projection method used (standard, differential, or kernel eigenspace), in the projection algorithm employed, in the use of simple or differential images before/after projection, and in the similarity matching criterion or classification method employed. The aim of this paper is to present an independent comparative study among some of the main eigenspace-based approaches. We believe that carrying out independent studies is relevant, since comparisons are normally performed using the implementations of the research groups that have proposed each method, which does not consider completely equal working conditions for the algorithms. Very often, a contest between the abilities of the research groups rather than a comparison between methods is performed. This study considers theoretical aspects as well as simulations performed using the Yale Face Database, a database with few classes and several images per class, and FERET, a database with many classes and few images per class.

Ageing, Health and Retirement in Europe: Alternative Scenarios for Health, Life Expectancy and Social Expenditure

This study deals with the impact of ageing populations and changes in their health status on health care and the utilization of long-term care services. Two kinds of projection methods have been used to estimate increases up to 2050 in the number of hospital cases and days, contacts with doctors, long-term care recipients and severely hampered persons for Belgium, Denmark, Finland, France, Germany, the Netherlands, Spain and the UK. In the first projection method, health care utilization data from national sources (which cover the whole population) are combined with two demographic scenarios. This kind of projection shows the impact of demographic change and increasing life expectancy on the utilization of health care services. In the second projection method, data from the European Community Household Panel are used (which only includes persons aged 16 but allows differentiation of utilization data by health status) and combined with four demographic and health scenarios.The two projection methods generally point to the same findings: changes in the number of hospital days and in the demand for long-term care-giving (i.e. the number of severely hampered persons) are likely to be stronger than changes in the number of hospital admissions and contacts with doctors; an additional increase in life expectancy leads to higher population figures by 2050, but increases in the utilization of health care services are more dynamic; and for the most part, countries with decreasing populations by 2050 do not show lower increases in the utilization of health care services than countries with increasing populations.Improvements in health status lead to a more moderate increase in the utilization of health care services compared with the scenarios that show no improvements in health. But in general, given the underlying assumptions improvements in health cannot completely compensate for the effect of increasing life expectancy.

ANALYSIS AND COMPARISON OF EIGENSPACE-BASED FACE RECOGNITION APPROACHES

Different eigenspace-based approaches have been proposed for the recognition of faces. They differ mostly in the kind of projection method being used and in the similarity matching criterion employed. The aim of this paper is to present a comparative study between some of these different approaches. This study considers theoretical aspects as well as experiments performed using a face database with a few number of classes (Yale) and also with a large number of classes (FERET).