In this paper, an original reduction algorithm for solving simultaneous multivariate polynomial equations is presented. The exponential in complexity, but the well-known algorithms, such as extended Euclidean and Buchberger's algorithm, are superexponential. superexponential complexity of algorithms due to their not being "minimal" a certain sense. produces Groebner basis. proposed achieves req...

The problems of polynomial interpolation with several variables present more difficulties than those one-dimensional interpolation. first problem is to study the regularity schemes. In fact, it well-known that, in contrast univariate case, there no universal space polynomials which admits unique Lagrange for all point sets a given cardinality, and so will depend on set <math xmlns="http://www.w...

In this paper, we develop an optimization-based approach to multivariate Chebyshev approximation on a finite grid. We consider two models: polynomial and generalized rational approximation. the second case, approximations are ratios of linear forms basis functions not limited monomials. It is already known that in case grid corresponding optimization problems can be reduced solving programming ...