A parameter estimation problem for ellipsoid fitting in the presence of measurement errors is considered. The ordinary least squares estimator is inconsistent, and due to the nonlinearity of the model, the orthogonal regression estimator is inconsistent as well, i.e., these estimators do not converge to the true value of the parameters, as the sample size tends to infinity.A consistent estimato...

A function based nonlinear least squares estimation (FNLSE) method is proposed and investigated in parameter estimation of Jelinski–Moranda software reliability model. FNLSE extends the potential fitting functions of traditional least squares estimation (LSE), and takes the logarithm transformed nonlinear least squares estimation (LogLSE) as a special case. A novel power transformation function...

This paper introduces tensor methods for solving large, sparse nonlinear least squares problems where the Jacobian either is analytically available or is computed by nite diier-ence approximations. Tensor methods have been shown to have very good computational performance for small to medium-sized, dense nonlinear least squares problems. In this paper we consider the application of tensor metho...

two multivariate calibration methods are compared for the simultaneous chromatographic determination and separation of sulfamethoxazole (smx) and phthalazine (phz) by high performance liquid chromatography (hplc). multivariate calibration techniques such as classical least squares (cls) and inverse least squares (ils) were introduced into hplc to determine the quantification by using uv detecto...

We present an approach for modeling and filtering digitally scanned images. The digital contour of an image is segmented to identify the linear segments, the nonlinear segments and critical corners. The nonlinear segments are modeled by B-splines. To remove the contour noise, we propose a weighted least q m s model to account for both the fitness of the splines as well as their approximate cur...

A least-squares mixed nite element formulation is applied to the nonlinear elliptic problems arising in each time-step of an implicit Euler discretization for variably saturated ow problems. This approach simultaneously constructs approximations to the ux in Raviart-Thomas spaces and to the hydraulic potential by standard H 1-conforming linear nite elements. Two important properties of the leas...

A comparison of two nonlinear input-output models describing the relationship between human emotion (excitement, frustration and engagement/boredom) signals and a virtual 3D face feature (distance-between-eyes) is introduced in this paper. A method of least squares with projection to stability domain for the building of stable models with the least output prediction error is proposed. Validatio...

In this paper, we first get further consideration of the order perturbation with normwise condition number MTLS problem. For easy estimation, show a lower bound for which is proved to be optimal. overcome problems encountered in calculating number, give an upper computing more effectively and nonstandard unusual bounds Both two types can enjoy storage computational advantages. getting insight i...