Yuan Xu. Common zeros of polynomials in several variables and higher dimensional quadrature

New York: Chapman & Hall/CRC, 1994. — 135 p.Presents a systematic study of the common zeros of polynomials in several variables which are related to higher dimensional quadrature. The author uses a new approach which is based on the recent development of orthogonal polynomials in several variables and differs significantly from the previous ones based on algebraic ideal theory. Featuring a great deal of new work, new theorems and, in many cases, new proofs, this self-contained work will be of great interest to researchers in numerical analysis, the theory of orthogonal polynomials and related subjectsPreliminaries and lemmas
Motivations
Common zeros of polynomials in several variables: first case
Moller's lower bound for cubature formula
Examples
Common zeros of polynomials in several variables: general case
Cubature formulae of even degree
Final discussions