Finding discontinuities of piecewise-smooth functions.
Finite element derivative interpolation recovery technique and superconvergence
A new finite element derivative recovery technique is proposed by using the polynomial interpolation method. We show that the recovered derivatives possess superconvergence on the recovery domain and ultraconvergence at the interior mesh points for finite element approximations to elliptic boundary problems. Compared with the well-known Z-Z patch recovery technique, the advantage of our method is that it gives an explicit recovery formula and possesses the ultraconvergence for the odd-order finite...
Functional equations stemming from numerical analysis [Book]
Geometrical/Geographical Optimization and Fast Automatic Differentiation
Improved Estimates of Statistical Regularization Parameters in Fourier Differentiation and Smoothing.
Interpolation and integration based on averaged values
We discuss recent results on constructing approximating schemes based on averaged values of the approximated function f over linear segments. In particular, we describe interpolation and integration formulae of high algebraic degree of precision that use weighted integrals of f over non-overlapping subintervals of the real line. The quadrature formula of this type of highest algebraic degree of precision is characterized.
Kolmogorov problem in and extremal Zolotarev ω-splines [Book]
Konvergenz optimaler Differentiationsformeln.
La différentiation automatique et son utilisation en optimisation
In this work, we present an introduction to automatic differentiation, its use in optimization software, and some new potential usages. We focus on the potential of this technique in optimization. We do not dive deeply in the intricacies of automatic differentiation, but put forward its key ideas. We sketch a survey, as of today, of automatic differentiation software, but warn the reader that the situation with respect to software evolves rapidly. In the last part of the paper, we present some...
Monotonicity and Error Bounds in Schemes of Romberg Type for the Computation of f(n) (0) by Central Differences and Extrapolation.
Newton Interpolation Is Efficient for Approximation of Linear Functionals.
Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials
Numerical Differentation of Functions of Very Many Variables.
Numerical Differentiation Procedures for Non-Exact Data.
Numerical Iteration of Functions of Very Many Variables.
Numerical Solution of Fractional Diffusion-Wave Equation with two Space Variables by Matrix Method
Mathematics Subject Classi¯cation 2010: 26A33, 65D25, 65M06, 65Z05.In the present paper we solve space-time fractional diffusion-wave equation with two space variables, using the matrix method. Here, in particular, we give solutions to classical diffusion and wave equations and fractional diffusion and wave equations with different combinations of time and space fractional derivatives. We also plot some graphs for these problems with the help of MATLAB routines.
On a Computational Method for the Second Fundamental Tensor and its Application to Bifurcation Problems.
On orthogonal decomposition of two-dimensional vector fields
On the asymptotics of mean value points for some finite-difference operators.
On the optimization of initial conditions for a model parameter estimation
The design of an experiment, e.g., the setting of initial conditions, strongly influences the accuracy of the process of determining model parameters from data. The key concept relies on the analysis of the sensitivity of the measured output with respect to the model parameters. Based on this approach we optimize an experimental design factor, the initial condition for an inverse problem of a model parameter estimation. Our approach, although case independent, is illustrated at the FRAP (Fluorescence...