Cubature formulae of fixed degree using the minimum number of nodes, the common zeros of a set of polynomials, are constructed by a number of techniques based on the theory of polynomial ideals.

A polynomial is a chain of algebraic terms with various values of powers. There are some words and phrases to look out for when you're dealing with polynomials: \(6{x^5} - 3{x^2} + 7\) is a polynomial ...

The paper discusses both theoretical properties and practical implementation of product integration rules of the form $$\int^\infty_{-\infty} k(x)f(x) dx \approx \sum ...

Polynomial equations are a cornerstone of modern science, providing a mathematical basis for celestial mechanics, computer graphics, market growth predictions and much more. But although most high ...

A sum rule is an identity connecting the entropy of a measure with the coefficients involved in the construction of its orthogonal polynomials, or Jacobi coefficients. In previous works we developed a ...

Complexity theory is a fundamental branch of theoretical computer science that categorises computational problems according to their inherent difficulty and the resources required to solve them. At ...

If \((x \pm h)\) is a factor of a polynomial, then the remainder will be zero. Conversely, if the remainder is zero, then \((x \pm h)\) is a factor. Often ...