Research On Interpolation And Convergence Of The Bernstein-Bezicr Coefficient And The Radial Basis Function Neural Network

The interpolation and the convergence of Bernstein-Bezier Coefficient and the RBF neural network are studied in this thesis. Comparing with one dimension, we research the interpolation and the convergence of multiple BB coefficient difficultly, which leads to progress slowly. Thus, we are worth researching the interpolation and the convergence of multiple BB coefficient. Since, the calculated amounts of the multidimensional issue are heavy, it is difficult to guarantee the uniqueness of interpolation, the convergence of the multivariate function has direction. For this reason, the interpolation and the convergence of ridge basis BB coefficient are discussed principally in this thesis.In chapter2, we discuss the expression of multiple Bezier polynomial, and prove the BB-coefficients an,k converge uniformly to g at the rate1/n, respectively. In section3, we consider the degree elevation formula for the BB-coefficients of multivariate Bernstein form polynomials and we discuss the degree-raised BB-coefficients an+r,q(r) of g converge uniformly to g at the rate1/n. Since An(g) and g are partial differential, we can study the uniform convergence of the partial derivatives of An(g) to the corresponding partial derivatives of g in section4. In the fifth chapter, we research the interpolation of the RBF neural network by using the ridge Bernstein polynomials, and structure the Lagrange interpolation basis function, the Newton interpolation formula and the Hilbert interpolation formula on the BB coefficients. In chapter6, we construct Bernstein polynomials with ridge form with least degree allowing a unique interpolation.