The focus of this paper is on conditional stability estimates for illposed inverse problems in partial differential equations. Conditional stability estimates have been obtained in the literature by a couple different methods. In this paper we propose a method called interpolation method, which is based on interpolation in variable Hilbert scales. We are going to work out the theoretical backgr...

Natural neighbor interpolation is a powerful method for data estimation in geoscience applications where measurements are scattered. However, this method is not easy to implement, and some simple implementations are numerically unstable. We describe a stable and fast implementation and make some in-depth comparisons with existing implementations.

INTERNODES is a general method to deal with non-conforming discretizations of second order partial differential equations on regions partitioned into two or several subdomains. It exploits two intergrid interpolation operators, one for transfering the Dirichlet trace across the interface, the others for the Neumann trace. In this paper we provide several interpretations of the method and we car...

We consider three steps numerical integrator which is derived by collocation and interpolation of power series approximation solution to generate a linear multistep method which serves as the corrector. The corrector is then implemented in block method. We then propose another numerical integrator which is implemented in block method to serve as a constant order predictor to the corrector. Basi...

A novel approach for teaching interpolation in the introductory course in numerical analysis is presented. The interpolation problem is viewed as a problem in linear algebra, whence the various forms of the interpolating polynomial are seen as different choices of a basis to the subspace of polynomials of the corresponding degree. This approach enables the instructor to relate this topic to the...

Numerical schemes using locally discontinuous polynomial approximation are very popular for high order approximation of conservation laws. While the most widely used numerical schemes under this paradigm appears to be the Discontinuous Galerkin method, the Spectral Difference scheme has often been found attractive as well, because of its simplicity in formulation and implementation. Linear stab...

Stationary interpolatory subdivision schemes which preserve shape properties such as convexity or monotonicity are constructed. The schemes are rational in the data and generate limit functions that are at least C 2. The emphasis is on a class of six-point convexity preserving subdivision schemes that generate C 2 limit functions. In addition, a class of six-point monotonicity preserving scheme...

A range restricted C interpolation local scheme to scattered data is derived. Each macro triangle of the triangulated domain is split into three mini triangles and the interpolating surface on each mini triangle is a cubic Bézier triangle. Sufficient conditions derived for the non-negativity of these cubic Bézier triangles are expressed as lower bounds to the Bézier ordinates. The non-negativit...

Recently, the convolution of the sinc kernel with the infinite sequence of a periodic function was expressed as a finite summation. The expression obtained, however, is not numerically stable when evaluated at or near integer values of time. This correspondence presents a numerically stable formulation equivalent to the results reported in the above cited paper and which, when sampled, is also ...

We use the connection between automata and logic to prove that a wide class of coalgebraic fixpoint logics enjoys uniform interpolation. To this aim, first we generalize one of the central results in coalgebraic automata theory, namely closure under projection, which is known to hold for weak-pullback preserving functors, to a more general class of functors, i.e.; functors with quasi-functorial...