When the modification is cast as an additional forcing term on the original structure a system of multivariate polynomials in the parameters of the beam cross-section are revealed.
For multiple players, determining the Pareto-optimal equilibrium in mixed strategies amounts to solving a system of multivariate polynomial equations of high order [13] and, as a rule, does not have an explicit solution.
We now explain the technique of multivariate polynomial interpolation of a single Boolean function B i. Therefore i ∈ {1, 2,..., N} is fixed and for the sake of simplicity the subscript i is omitted.
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.
Thus, a surrogate model is devised, by approximating the trench parameters as multivariate polynomial functions of three dimensionless variables of the SCR.
We describe the design, implementation and experimental evaluation of new algorithms for computing the approximate factorization of multivariate polynomials with complex coefficients that contain numerical noise.
Ritt Wuʼs algorithm of characteristic sets is the most representative for triangularizing sets of multivariate polynomials.
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.
To fully understand the technical details of our analysis, very basic knowledge in linear algebra and algebra of multivariate polynomials is required.
In these problems, we show how the design equations can be written as multivariate polynomial systems of equations and accordingly how Gröbner algorithms offer an effective way to obtain solutions in some of these cases.
