We consider the guaranteed a posteriori estimates for the inverse parabolic operators with homogeneous initial-boundary conditions. Our estimation technique uses a full-discrete numerical scheme, which is based on the Galerkin method with an interpolation in time by using the fundamental solution for semidiscretization in space. In our technique, the constructive a priori error estimates for a ...

This paper mainly aims at solving the problems of sampled data synchronization in digital substation based on Filed Programable Gate Array (FPGA). Compared with traditional substations, the design achieves data synchronization without connecting an external clock. Synchronization algorithm is based on Newton interpolation algorithm. The system consists of multi-channel data sampling module, syn...

This paper introduces a new class of quasi-Newton algorithms for unconstrained minimization in which no line search is necessary and the inverse Hessian approximations are positive definite. These algorithms are based on a two-parameter family of rank two, updating formulae used earlier with line search in self-scaling variable metric algorithms. It is proved that, in a quadratic case, the new ...

An iterative univariate minimizer (line search) is often used to generate a steplength in each step of a descent method for minimizing a multivariate function. The line search performance strongly depends on the choice of the stopping rule enforced. This termination criterion and other algorithmic details also affect the overall efficiency of the multivariate minimization procedure. Here we pro...

It has been known that an efficient approach to the determination of the convex best C-spline interpolant to a set of given data is to solve its unconstrained dual program by standard numerical methods (e.g., Newton’s method.) Regularity and well-posedness of the dual program, which are two important issues but not well-addressed in the literature, are focus of the paper. Our well-posedness res...

This paper is devoted to prove the unbounded divergence on superdense sets, with respect to product quadrature formulas of interpolatory type on Jacobi nodes. Mathematics Subject Classification (2010): 41A10, 41A55, 65D32.

Orthogonal polynomials of different kinds as the basic tools play very important role in construction and analysis of quadrature formulas of maximal and nearly maximal algebraic degree of exactness. In this survey paper we give an account on some important connections between orthogonal polynomials and Gaussian quadratures, as well as several types of generalized orthogonal polynomials and corr...