An accelerated least-squares approach is introduced in this work by incorporating a greedy point selection method with randomized singular value decomposition (rSVD) to reduce the computational complexity of missing data reconstruction. The rSVD used speed up computation low-dimensional basis that required for projection employing randomness generate small matrix instead large from high-dimensi...

This paper presents a new method based on adaptive filtering theory for superresolution restoration of continuous image sequences. The proposed methodology suggests least squares (LS) estimators which adapt in time, based on adaptive filters, least mean squares (LMS) or recursive least squares (RLS). The adaptation enables the treatment of linear space and time-variant blurring and arbitrary mo...

we present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with lr fuzzy variables. as solutions, notions of exact and approximate solutions are considered. we transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. if the corresponding crisp system is incompatible, then the fuzzy ...

This paper furnishes two classes of methods for calculating the best approximate solution of an operator equation in Banach spaces, where the operator is bounded, linear and has closed range. The best approximate solution can be calculated by an iterative method in Banach spaces stated in terms of an operator parameter. Specifying the parameter yields some new and some old iterative techniques....

Least Squares Support Vector Machines (LS-SVMs) were proposed by replacing the inequality constraints inherent to L1-SVMs with equality constraints. So far this idea has only been suggested for a least squares (L2) loss. We describe how this can also be done for the sumof-slacks (L1) loss, yielding a new classifier (Least 1-Norm SVMs) which gives similar models in terms of complexity and accura...

Building a calibration model with detection and quantification capabilities is identical to the task of building a regression model. Although commonly used by analysts, an application of the calibration model requires at first careful attention to the three components of the regression triplet (data, model, method), examining (a) the data quality of the proposed model; (b) the model quality; (c...

In this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. In additional, the least-squares method is adopted tond the solution. To regularize the resultant ill-conditioned linear system ofequations, we apply the Tikhonov regularization method to obtain the stablenumerical approximation to the solution. Some numerical experiments con-rm the utility of th...

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that in the univariate case and for the uniform distribution, the least-squares method is optimal in expectation in [1] and in probability in [7]...