Search results for "Lagrange polynomial"
showing 3 items of 3 documents
Residuenabschätzung für Polynom-Nullstellen mittels Lagrange-Interpolation
1970
If, for each zero of a polynomial, an approximation is known, estimates for the errors of these approximations are given, based on the evaluation of the polynomial at these points. The procedure can be carried over to the case of multiple roots and root clusters using derivatives up to the orderk - 1, wherek is the multiplicity of the cluster.
Weighted Extrapolation Techniques for Finite Difference Methods on Complex Domains with Cartesian Meshes
2016
The design of numerical boundary conditions in high order schemes is a challenging problem that has been tackled in different ways depending on the nature of the problem and the scheme used to solve it numerically. In this paper we propose a technique to extrapolate the information from the computational domain to ghost cells for schemes with structured Cartesian Meshes on complex domains. This technique is based on the application of Lagrange interpolation with weighted filters for the detection of discontinuities that permits a data dependent extrapolation, with high order at smooth regions and essentially non oscillatory properties near discontinuities. This paper is a sequel of Baeza et…
On specific stability bounds for linear multiresolution schemes based on piecewise polynomial Lagrange interpolation
2009
Abstract The Deslauriers–Dubuc symmetric interpolation process can be considered as an interpolatory prediction scheme within Harten's framework. In this paper we express the Deslauriers–Dubuc prediction operator as a combination of either second order or first order differences. Through a detailed analysis of certain contractivity properties, we arrive to specific l ∞ -stability bounds for the multiresolution transform. A variety of tests indicate that these l ∞ bounds are closer to numerical estimates than those obtained with other approaches.