Multivariate vertex splines and finite elements
Journal of Approximation Theory
Explicit error bounds for the derivatives of piecewise-Lidstone interpolation
Journal of Computational and Applied Mathematics
Lidstone approximation on the triangle
Applied Numerical Mathematics
Polynomial approximation of CM functions by means of boundary values and applications: A survey
Journal of Computational and Applied Mathematics
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For a function f ∈ C2n+1 ([a,b]) an explicit polynomial interpolant in a and in the even derivatives up to the order 2n - 1 at the end-points of the interval is derived. Explicit Cauchy and Peano representations and bounds for the error are given and the analysis of the remainder term allows to find sufficient conditions on f so that the polynomial approximant converges to f. These results are applied to derive a new summation formula with application to rectangular quadrature rule. The polynomial interpolant is related to a fairly interesting boundary value problem for ODEs. We will exhibit solutions for this problem in some special situations.