The presence of endogenous variables in the statistical models leads to inconsistent and bias estimators for the parameters. In this case, several approaches have been proposed which are able to tackle the biase and inconsistency problems only in large sample situations. One of these METHODs is biased on instrumental variables which causes removing endogenous variables. The METHOD of TWO-STAGE LEAST SQUAREs is another approach in this case that it has more accurate than ordinary LEAST SQUAREs.This paper aims to enhance the accuracy of three METHODs of estimation based upon LEAST SQUARE METHODology called, TWO-STAGE iterative LEAST SQUAREs, TWO-STAGE Jackknife LEAST SQUAREs and also TWO-STAGE calibration LEAST SQUAREs. In order to evaluate the performance of each METHOD, a simulation study is conducted. Also, using data collected in 1390 related to the cost and revenue in Iran, those METHODs to estimate parameters are compared.

A meshless approach, collocation discrete LEAST SQUARE (CDLS) METHOD, is extended in this paper, for solving elasticity problems. In the present CDLS METHOD, the problem domain is discretized by distributed field nodes. The field nodes are used to construct the trial functions. The moving LEAST-SQUAREs interpolant is employed to construct the trial functions. Some collocation points that are independent of the field nodes are used to form the total residuals of the problem. The LEAST-SQUAREs technique is used to obtain the solution of the problem by minimizing the summation of the residuals for the collocation points. The final stiffness matrix is symmetric and therefore can be solved via efficient solvers. The boundary conditions are easily enforced by the penalty METHOD. The present METHOD does not require any mesh so it is a truly meshless METHOD. Numerical examples are studied in detail, which show that the present METHOD is stable and possesses good accuracy, high convergence rate and high efficiency.

Given by economic growth and development theories, agriculture sector is the important and it can prove to increase of industrial production.Agriculture sector can cover the needed input of industry such as labor and capital stock. Also agriculture sector is a main market of industrial production.Thus to attention of difference between productivity and spillover of both section that made a supplement relationship between sections. Therefore to aim evaluating past policies and planning for future policies, it's necessary to recognize this relationship. So in this paper studied relation between Agriculture and Industry sectors in Iran's economy by using time series data 1978-2001 and Ordinary LEAST SQUARE and TWO STAGE LEAST SQUARE METHODs. Then relation of value-added growth of industry sector and Oil crops production considered as part of agriculture sector that it's related with industry. Finally effect of capital and labor on value-added of agriculture and industry sectors discussed. As shown results, the bilateral relation has a useful for agricultural sector whereas Oi1cropsproduction couldn't have influence on proving of industry sector.

A dual-time implicit mesh-less METHOD is presented for unsteady compressible flow calculations. Polynomial LEAST-SQUARE (PLS) and Taylor series LEAST-SQUARE (TLS) procedures are used to estimate the spatial derivatives at each node and their computational efficiencies are compared. Also, the effect of the neighbor stencil selection on the accuracy of the METHOD is investigated. As a new approach, different neighboring stencils are used for the highly stretched point distribution inside the boundary layer region and the inviscid isotropic point distribution outside this area. The unsteady flows over stationary and moving objects at subsonic and transonic flow conditions are solved. Results indicate the computational efficiency of the METHOD in comparison with the alternative approaches. The convergence histories of the flow solution show that the PLS METHOD is computationally faster than TLS METHOD. In addition, the eight point neighboring stencil inside the viscous region is more efficient than other choices.

Many meshless METHODs are presented in recent years for solving partical differential equations. All of them use a background mesh to introducing the Guossian points for solution of the integral equation. Numerical integration has significant effects on convergence and accuracy of solution from many meshless METHODs. They are meshless only from the point of view of interpolation of the field variables. In this paper we present a fully meshless procedure for linear and nonlinear convection-diffusion equation problems in steady and transient forms. In this new METHOD a fully LEAST SQUAREs METHOD is used in both function approximation and the discretization of the governing differential equations. The discritized equations are obtained via a discrete LEAST SQUAREs METHOD in which the sum of the SQUAREd residuals are minimized with respect to unknown nodal parameters in the inner and boundary nodes. In this process no numerical integration is needed and the obtained equations are symmetric and positive definite. The shape functions are derived using the moving LEAST SQUAREs (MLS) METHOD of function approximation with a spline weighting function. The convergency and accuracy of the METHOD is programmed using visual Fortran 6.5and accuracy of the results are compared and verified with reference to some examples.

LEAST SQUARE matching (LSM) is one of the most accurate image matching METHODs in photogrammetry and remote sensing. The main disadvantage of the LSM is its high computational complexity due to large size of observation equations. To address this problem, in this paper a novel METHOD, called fast LEAST SQUARE matching (FLSM) is being presented. The main idea of the proposed FLSM is decreasing the size of the observation equations to improve the efficiency of the matching process. For this purpose, the pixels in the matching window are ordered using a special robustness measure. Then, a specific percent of the pixels with the highest robustness is selected for matching process. The phase congruency and entropy measures are used to compute the proposed robustness measure. The proposed FLSM METHOD was successfully applied to match various synthetic and real image pairs, and the results demonstrate its capability to increase matching efficiency. The matching results show that the proposed FLSM METHOD is three times faster than standard LSM METHOD.

In this research, a linear combination of moving LEAST SQUARE (MLS) and local radial basis functions (LRBFs) is considered within the framework of the meshless METHOD to solve the TWO-dimensional hyperbolic telegraph equation. Besides, the differential quadrature METHOD (DQM) is employed to discretize temporal derivatives. Furthermore, a control parameter is introduced and optimized to achieve minimum errors via an experimental approach. Illustrative examples are provided to demonstrate the applicability and efficiency of the METHOD. The results prove the superiority of this METHOD over using MLS and LRBF individually.

In this paper, we propose the LEAST-SQUAREs METHOD for computing the positive solution of a m´n fully fuzzy linear system (FFLS) of equations, where m>n, based on Kaman's arithmetic operations on fuzzy numbers that introduced in [18]. First, we consider all elements of coefficient matrix are non-negative or non-positive. Also, we obtain 1-cut of the fuzzy number vector solution of the non-SQUARE FFLS of equations by using pseudoinverse.If 1-cuts vector is non-negative, we solve constrained LEAST SQUAREs problem for computing left and right spreads. Then, in the special case, we consider 0 is belong to the support of some elements of coefficient matrix and solve three overdetermined linear systems and if the solutions of these systems held in non-negative fuzzy solutions then we compute the solution of the non-SQUARE FFLS of equations. Else, we solve constrained LEAST SQUAREs problem for obtaining an approximated non-negative fuzzy solution. Finally, we illustrate the efficiency of the proposed METHOD by solving some numerical examples.

In this paper, the Mixed Discrete LEAST SQUAREd Meshless (MDLSM) METHOD is used for solving quadratic Partial Dierential Equations (PDEs). In the MDLSM METHOD, the domain is discretized only with nodes, and a minimization of a LEAST SQUAREs functional is carried out. The LEAST SQUARE functional is de ned as the sum of the residuals of the governing dierential equation and its boundary condition at the nodal points. In MDLSM, the main unknown parameter and its rst derivatives are approximated independently with the same Moving LEAST SQUAREs (MLS) shape functions. The solution of the quadratic PDE does not, therefore, require calculation of the complex second order derivatives of MLS shape functions. Furthermore, both Neumann and Dirichlet boundary conditions can be treated and imposed as a Dirichlet type boundary condition, which is applied using a penalty METHOD. The accuracy and eciency of the MDLSM METHOD are tested against three numerical benchmark examples from one-dimensional and TWO-dimensional PDEs. The results are produced and compared with the irreducible DLSM METHOD and exact analytical solutions, indicating the ability and eciency of the MDLSM METHOD in ecient and eective solution of quadratic PDEs.