Lagrange Coefficients Research Articles

On using the Lagrange coefficients for a posteriori error estimation

A posteriori error estimation of the objective functional is considered by means of a differential presentation of a finite-difference scheme and adjoint equations. The local approximation error is presented as a Taylor series remainder in the Lagrangian form. The field of the Lagrange coefficients is determined by a high-accuracy finite-difference template affecting the computation results. The feasibility of using the Lagrange coefficients for refining the solution and for estimating its uncertainty is considered.

The convergence of partial sums of interpolating polynomials

For functions of ΛBV, we study the convergence of the partial sums of interpolating polynomials. An estimate is found for the Fourier–Lagrange coefficients of these functions. For functions in BV, convergence is shown at points of discontinuity if the order of the polynomial increases sufficiently rapidly compared to the order of the partial sum. A Dirichlet–Jordan type theorem is shown for functions of harmonic bounded variation, and this result is shown to be best possible.

Fundamental polynomials of Lagrange interpolation and coefficients of mechanical quadrature

Fundamental polynomials of Lagrange interpolation and coefficients of mechanical quadrature