Sinusoidal model and its variants are commonly used in speech processing. In the literature, there are various methods for the estimation of the unknown parameters of sinusoidal model such as Fourier transform based on FFT algorithm and Least Squares (LS) method. Least Squares method is more accurate and actually optimum for Gaussian noise, thus, more appropriate for high-quality signal process...

In many applications we want to find an approximation for a function, for example for differential equations. Example problem: We want to understand how a calculator or computer can evaluate sinx for a given value x. The processor can essentially only perform addition, multiplication, division. Therefore we can try to approximate the function with a polynomial. We use the notation Pn for polyno...

Numerical solutions obtained by the Meshless Local Petrov-Galerkin (MLPG) method are presented for two dimensional steady-state heat conduction problems. The MLPG method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. The penalty method is adopted to efficiently enforce the essential boundary co...

We construct symmetric polar WAMs (Weakly Admissible Meshes) with low cardinality for least-squares polynomial approximation on the disk. These are then mapped to an arbitrary triangle. Numerical tests show that the growth of the least-squares projection uniform norm is much slower than the theoretical bound, and even slower than that of the Lebesgue constant of the best known interpolation poi...

Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets n be the number of constraints and d be the number of variables, with n d. Then, existing exact methods find a solution vector in O(nd2) time. We present two randomized algorithms that provide accurate relative-error approximations...

The isogeometric collocation method (IGA-C), which is a promising branch of analysis (IGA), can be considered fitting the load function with combination numerical solution and its derivatives. In this study, we develop an iterative method, least-squares progressive-iterative approximation (IG-LSPIA), to solve problem in method. IG-LSPIA starts initial blending function, where control coefficien...

In comparison to the original SVM, which involves a quadratic programming task; LS–SVM simplifies the required computation, but unfortunately the sparseness of standard SVM is lost. Another problem is that LS-SVM is only optimal if the training samples are corrupted by Gaussian noise. In Least Squares SVM (LS–SVM), the nonlinear solution is obtained, by first mapping the input vector to a high ...

A simple and rapid method for the determination of 137Ba isotope abundances in water samples by inductively coupled plasma-optical emission spectrometry (ICP-OES) coupled with least-squares support vector machine regression (LS-SVM) is reported. By evaluation of emission lines of barium, it was found that the emission line at 493.408 nm provides the best results for the determination...