This paper introduces a novel method for solving the generalized total Least squares problem, an extension of the total Least squares problem. The generalized total Least squares problem emerges when solving overdetermined linear systems with the multiple right-hand sides $\mathbf{AX} \thickapprox \mathbf{B}$, where both the observation matrix $\mathbf{B}$ and the data matrix $\mathbf{A}$ contain errors. Our approach involves extending the Taylor series expansion to reformulate the generalized total Least squares problem into a linear problem, allowing us to employ the tensor form of the generalized Least squares algorithm for efficient computation. This technique streamlines the computational process and enhances solution accuracy. For a more detailed survey, we compare the proposed method for solving the generalized total Least squares problem with one of the matrix format methods for the associated total Least squares problem. Empirical results show that our method significantly improves computational efficiency and solution precision. Additionally, we demonstrate its practical application in the context of image blurring.

The Mixed Least squares Meshfree (MDLSM) method has shown its appropriate efficiency for solving Partial Differential Equations (PDEs) governing the engineering problems. The method is based on the minimizing the residual functional. The residual functional is defined as a summation of the weighted residuals on the governing PDEs and the boundaries. The Moving Least squares (MLS) is usually applied in the MDLSM method for constructing the shape functions. Although the required consistency and compatibility for the approximation function is satisfied by the MLS, the method loss its appropriate efficiency when the nodal points cluster too much. In the current study, the mentioned drawback is overcome using the novel approximation function called Mapped Moving Least squares (MMLS). In this approach, the cluster of closed nodal points maps to standard nodal distribution. Then the approximation function and its derivatives compute noting the some consideration. The efficiency of suggested MMLS for overcoming the drawback of MLS is evaluated by approximating the mathematical function. The obtained results show the ability of suggested MMLS method to solve the drawback. The suggested approximation function is applied in MDLSM method, and used for solving the Burgers equations. Obtained results approve the efficiency of suggested method.

This study compared the performance of the partial Least squares-structural equation modelling (PLS-SEM) and the robust partial Least squares-structural equation modelling (RPLS-SEM) methods through Winsorisation approach The inputs and the outputs used in this model were based on the electricity generation data, derived from the Al-Zawiya Steam Power Plant, Libya. Furthermore, the researchers compared the novel RPLS-SEM approach with the traditional PLS-SEM approach and noted that the novel RPLS-SEM method was more efficient compared to PLS-SEM.

Pedomodels have become a popular topic in soil science and environmental research. They are predictive functions of certain soil properties based on other easily or cheaply measured properties. The common method for fitting pedomodels is to use classical regression analysis, based on the assumptions of data crispness and deterministic relations among variables. In modeling natural systems such as soil system, in which the above assumptions are not held true, prediction is influential and we must therefore attempt to analyze the behavior and structure of such systems more realistically. In this paper we consider fuzzy Least squares regression as a means of fitting pedomodels. The theoretical and practical considerations are illustrated by developing some examples of real pedomodels.

In this paper, we propose a nonparametric rank-based alternative to the Least-squares independent component analysis algorithm developed. The basic idea is to estimate the squared-loss mutual information, which used as the objective function of the algorithm, based on its copula density version. Therefore, no marginal densities have to be estimated. We provide empirical evaluation of the proposed algorithm through simulation and real data analysis. Since the proposed algorithm uses rank values rather than the actual values of the observations, it is extremely robust to the outliers and suffers less from the presence of noise than the other algorithms.

Image magnification is one of the current issues of image processing in which keeping the quality and structure of images is the main concern. In image magnification, it is necessary to insert information in extra pixels. Adding information to an image should be compatible with the image structure with- out making artificial blocks. In this research, extra pixels are estimated using the surface of Least squares, and all the pixels are reviewed according to the suggested edge-improving algorithm. The suggested ethod keeps the edges and minimizes the magnified image opacity and the artificial blocks. Numerical results are presented by using PSNR and SSIM fidelity measures and compared to some other methods. The average PSNR of the original image and image zooming is 32.79 which it shows that image zooming is very similar to the original image. Experimental results show that the proposed method has a better performance than others and provides good image quality.

Determination of the diffusion coefficient on the base of solution of a linear inverse problem of the parameter estimation using the Least-square method is presented in this research. For this propose a set of temperature measurements at a single sensor location inside the heat conducting body was considered. The corresponding direct problem was then solved by the application of the heat fundamental solution.