Multivariate vertex splines and finite elements
Journal of Approximation Theory
Nonlinear Analysis: Theory, Methods & Applications
Explicit error bounds for the derivatives of piecewise-Lidstone interpolation
Journal of Computational and Applied Mathematics
Boundary-type quadrature and boundary element method
Journal of Computational and Applied Mathematics - Special issue: Approximation theory, wavelets, and numerical analysis
Journal of Computational and Applied Mathematics
Lidstone approximation on the triangle
Applied Numerical Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Interpolation to boundary data on the simplex
Computer Aided Geometric Design
Abel-Gontscharoff boundary value problems
Mathematical and Computer Modelling: An International Journal
On the bivariate Shepard-Lidstone operators
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
We collect classical and more recent results on polynomial approximation of sufficiently regular real functions defined in bounded closed intervals by means of boundary values only. The problem is considered from the point of view of the existence of explicit formulas, interpolation to boundary data, bounds for the remainder and convergence of the polynomial series. Applications to some problems of numerical analysis are pointed out, such as nonlinear equations, numerical differentiation and integration formulas, special associated differential boundary value problems. Some polynomial expansions for smooth enough functions defined in rectangles or in triangles of R^2 as well as in cuboids or in tetrahedrons in R^3 and their applications are also discussed.