Abstract M split estimation is a method that enables the of mutually competing versions parameters in functional observation models. In presented study, classical models found it are replaced by errors-in-variables (EIV) Similar to weighted total least-squares (WTLS) method, random components these were assigned covariance matrix Thus, proposed named Total (TM ) estimation, corresponds basic ru...

Let I[f ] = ∫ 1 −1 f(x) dx, where f ∈ C ∞(−1, 1), and let Gn[f ] = ∑n i=1 wnif(xni) be the n-point Gauss–Legendre quadrature approximation to I[f ]. In this paper, we derive an asymptotic expansion as n → ∞ for the error En[f ] = I[f ]−Gn[f ] when f(x) has general algebraic-logarithmic singularities at one or both endpoints. We assume that f(x) has asymptotic expansions of the forms f(x) ∼ ∞ ∑ ...

Gauss mixtures are a popular class of models in statistics and statistical signal processing because Gauss mixtures can provide good fits to smooth densities, because they have a rich theory, because they can yield good results in applications such as classification and image segmentation, and because the can be well estimated by existing algorithms such as the EM algorithm. We here use high ra...

| Superresolution reconstruction produces a high resolution image from a set of aliased low resolution images. We model the low resolution frames as blurred and down-sampled, shifted versions of the high resolution image. In many applications, the blurring process, i.e., point spread function (PSF) parameters of the imaging system, is not known. In our blind superresolution algorithm, we rst es...

The approach we follow consists in transforming the numerical evaluation of hypersingular integrals into the calculation of a nearly singular integral whose mass is distributed according to a positive parameter ε. To evaluate the latter we apply a Gauss quadrature formula associated with a nearly singular weight function. It is estimated the error in terms of ε. Some numerical results are prese...

Rates of convergence (or divergence) are obtained in the application of Gauss, Lobatto, and Radau integration rules to functions with an algebraic or logarithmic singularity inside, or at an endpoint of, the interval of integration. A typical result is the following: For a generalized Jacobi weight function on [-1,1], the error in applying an «-point rule to f(x) = \x -y\~* isO(n~2 + 2i), if y ...

It is shown that the Kronrod extension to the «-point Gauss integration rule, with respect to the weight function (1 x2)V~"2, 0 < M < 2, ju i= 1, is of exact precision 3n + 1 for n even and 3n + 2 for n odd. Similarly, for the (n-t-l)-point Lobatto rule, with — V¡ < M < 1, u ^ 0, the exact precision is 3n for n odd and 3n + 1 for n even.