in this article, the discrete time state space model with first-order autoregressive dependent process noise is considered and the recursive method for filtering, prediction and smoothing of the hidden state from the noisy observation is designed. the explicit solution is obtained for the hidden state estimation problem. finally, in a simulation study, the performance of the designed method ...

This paper is devoted to the convergence rate estimate for the method of successive subspace corrections applied to symmetric and positive semidefinite (singular) problems. In a general Hilbert space setting, a convergence rate identity is obtained for the method of subspace corrections in terms of the subspace solvers. As an illustration, the new abstract theory is used to show uniform converg...

A holomorphic representation of the Jacobi algebra hn⋊sp(n,R) by first order differential operators with polynomial coefficients on the manifold C × Dn is presented. The Hilbert space of holomorphic functions on which the holomorphic first order differential operators with polynomials coefficients act is constructed.

The simplicial volume introduced by Gromov provides a topologically accessible lower bound for the minimal volume. Lafont and Schmidt proved that the simplicial volume of closed, locally symmetric spaces of noncompact type is positive. In this paper, we extend this positivity result to certain non-compact locally symmetric spaces of finite volume, including Hilbert modular varieties. The key id...

This paper presents a robust method to correct for intensity differences across a series of aligned stained histological slices. The method is made up of two steps. First, for each slice, a scale-space analysis of the histogram provides a set of alternative interpretations in terms of tissue classes. Each of these interpretations can lead to a different classification of the related slice. A si...

A wide class of the operator equations F(u)= h in a Hilbert space is studied. Convergence of a Dynamical Systems Method (DSM), based on the continuous analog of the Newton method, is proved without any smoothness assumptions on the F ′(u). It is assumed that F ′(u) depends on u continuously. Existence and uniqueness of the solution to evolution equation u̇(t)=−[F ′(u(t))]−1(F (u(t))− h), u(0)= u...

We introduce a new approximation scheme combining the viscosity method with parallel method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a family of finitely strict pseudocontractions. We obtain a strong convergence theorem for the sequences generated by these processes in Hilbert spaces. Based on this result, we also g...

An iterative method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space has been studied. We prove a strong convergence theorem under mild assumptions.

This paper is concern with the boundary-value problem in the Hilbert space ) ( 2 N w l generated by an infinite Jacobi matrix with a spectral parameter in the boundary condition. We proved theorems on the completeness of the system of eigenvalues and eigenvectors of operator generated by boundary value problem.