Dual Polynomial Bases

On Polynomial Reproduction of Dual Fe Bases

New Bases for Polynomial-Based Spaces

Since it is well-known that the Vandermonde matrix is ill-conditioned, while the interpolation itself is not unstable in function space, this paper surveys the choices of other new bases. These bases are data-dependent and are categorized into discretely l2-orthonormal and continuously L2-orthonormal bases. The first one construct a unitary Gramian matrix in the space l2(X) while the late...

Type-II Optimal Polynomial Bases

In the 1990s and early 2000s several papers investigated the relative merits of polynomial-basis and normal-basis computations for F2n . Even for particularly squaring-friendly applications, such as implementations of Koblitz curves, normal bases fell behind in performance unless a type-I normal basis existed for F2n . In 2007 Shokrollahi proposed a new method of multiplying in a type-II normal...

Polynomial programming using Groebner Bases

Finding the global optimal solution for a general nonlinear program is a diicult task except for very small problems. In this paper we identify a class of non-linear programming problems called polynomial programming problems (PP). A polynomial program is an optimization problem with a scalar polynomial objective function and a set of polynomial constraints. By using Groebner Bases, we can dete...

Involutive Bases of Polynomial Ideals

In this paper we consider an algorithmic technique more general than that proposed by Zharkov and Blinkov for the involutive analysis of polynomial ideals. It is based on a new concept of involutive monomial division which is defined for a monomial set. Such a division provides for each monomial the self-consistent separation of the whole set of variables into two disjoint subsets. They are cal...