We consider the least-squares finite element method (lsfem) for systems of nonlinear ordinary differential equations, and establish an optimal error estimate this when piecewise linear elements are used. The main assumptions that vector field is sufficiently smooth local Lipschitz constant as well operator norm Jacobian matrix associated with nonlinearity small, restricted to a suitable neighbo...

We compare the risk of ridge regression to a simple variant of ordinary least squares, in which one simply projects the data onto a finite dimensional subspace (as specified by a principal component analysis) and then performs an ordinary (un-regularized) least squares regression in this subspace. This note shows that the risk of this ordinary least squares method (PCA-OLS) is within a constant...

A structural stability condition is sought for least squares linear prediction methods in the given data case. Save the Toeplitz case, the structure of the normal equation matrix yields no acknowledged guarantee of stability. Here, a new sufficient condition is provided, and several least squares prediction methods are shown to be structurally stable.

By incorporating temporal effects into the geographically weighted regression (GWR) model, an extended GWR model, geographically and temporally weighted regression (GTWR), has been developed to deal with both spatial and temporal nonstationarity simultaneously in real estate market data. Unlike the standard GWR model, GTWR integrates both temporal and spatial information in the weighting matric...

To evaluate and improve the quality of land surface albedo products, validation with ground measurements of albedo is crucial over the spatially and temporally heterogeneous land surface. One of the essential steps for satellite albedo product validation is coarse scale observation technique development with long time ground-based measurements. In this paper, the optimal nodes were selected fro...

This paper employs the Ordinary Least Squares, Instrumental Variables and Treatment Effect models to a new dataset from the Vietnam Household Living Standards Survey (VHLSS) to estimate return to four-year university education in 2008. Our estimates reveal that income premium of four-year university education is about 97 percent above that of high school education, and robust to the various est...

in this paper, least square method (lsm) and differential transformation method (dtm) are used to solve the problem of laminar nanofluid flow in a semi-porous channel in the presence of transverse magnetic field. due to existence some shortcomings in each method, a novel and efficient method named ls-dtm is introduced which omitted those defects and has an excellent agreement with numerical sol...

In recent years, the interest in the study of outlier robustness properties in Extreme Learning Machines (ELM) has grown. Most of the published works uses a more robust estimation method than the commonly adopted ordinary least squares. Nevertheless, the ELM network offers other challenges that also influence its robustness properties, such as the number of hidden neurons and the computational ...