In all these algorithms, multivariate polynomials are expanded in a monomial basis, and the computations mainly reduce to linear algebra.
Often all multivariate polynomials up to some total degree are included in the truncated expansion.
To fully understand the technical details of our analysis, very basic knowledge in linear algebra and algebra of multivariate polynomials is required.
In its basic version, it deals with multivariate polynomials over a field (k).
It was designed to provide efficient handling of multivariate polynomials, algebras and special functions that are needed for loop calculations in theoretical quantum field theory.
We find in the present study that combining polyharmonic splines (PHS) with multivariate polynomials offers an outstanding combination of simplicity, accuracy, and geometric flexibility when solving elliptic equations in irregular (or regular) regions.
In this paper, we present a fully complex-valued functional link network (CFLN) with multivariate polynomials as the nonlinear functions.
It is well known that the classical algebraic variety in algebraic geometry is to study geometrical properties of the common intersection of surfaces represented by multivariate polynomials.
Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropriate univariate polynomials.
