关键词:  , Lagrange插值, 收敛性, 逼近, 修正法

Abstract: To solve the problem that Lagrange interpolation polynomials do not uniformly converge for any continuous function, the
convergence is improved by the Bernstein-type operator with the one-point correction method and the trigonometric interpolation
polynomial operators and algebraic polynomial operator with the two-point correction method. The one-point correction method is used to construct an algebraic polynomial operator Fn ( f;x)（Bernstein-type operator）, two-point correction method is used to construct trigonometric interpolation polynomial operator Tn ( f; r, x)（ r is a natural number）, and algebraic polynomial operator Gn, R ( f; x)（ R is a natural number）, and a specific program is written in C language to analyze the superiority and inferiority of its approximation effects. The results show that compared with Lagrange interpolation polynomial operators, the Bernstein-type operator, trigonometric interpolation polynomial operator and algebraic polynomial operator optimized by the one-point correction method and the two-point correction method have faster running speed, smaller error values, and closer convergence results to the exact solution.

Key words: Lagrange interpolation, convergence, approach, correction method