Multivariate polynomial interpolation and meshfree differentiation via undetermined coefficients

Computational aspects of multivariate polynomial interpolation: Indexing the coefficients

An algorithm is derived for generating the information needed to pass efficiently between multiindices of neighboring degrees, of use in the construction and evaluation of interpolating polynomials and in the construction of good bases for polynomial ideals. short title: Indexing the coefficients of multivariate polynomials AMS (MOS) Subject Classifications: primary 41A05, 41A10, 41A63, 65D05, ...

On multivariate polynomial interpolation

We provide a map Θ 7→ ΠΘ which associates each finite set Θ of points in C with a polynomial space ΠΘ from which interpolation to arbitrary data given at the points in Θ is possible and uniquely so. Among all polynomial spaces Q from which interpolation at Θ is uniquely possible, our ΠΘ is of smallest degree. It is also Dand scale-invariant. Our map is monotone, thus providing a Newton form for...

Lectures on Multivariate Polynomial Interpolation

Computational aspects of multivariate polynomial interpolation

The paper is concerned with the practical implementation of two methods to compute the solution of polynomial interpolation problems. In addition to a description of the implementation, practical results and several improvements will be discussed, focusing on speed and robustness of the algorithms under consideration.

Obtaining exact interpolation multivariate polynomial by approximation

In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In order to improve the situation, exactly interpolating methods are often proposed for the exact results and approximate interpolating methods for the approximate...