【摘要】 研究插值多项式对|x|α达到最佳逼近度的一种构造方法,证明了对n=2m,m∈N,α∈(0,1],有Fn(α)<Cα(n+2)α,其中F2m(α)=max||x|α-Q2m(x)|,Q2m(x)是以第二类Chebyshev多项式的零点xj=cosjπ2m+2(j=1,2,-1 x 1…2m+1)为插值结点的对|x|α的Lagrange插值多项式,Cα是与α有关的常数.更多还原

【Abstract】 In the present paper we study the approximation of |x|~α on [-1,1] by interpolation polynomials. It is showed that: for n=2m,m∈N,α∈(0,1],F\-n(α)<C\-α(n+2)~α,where F(2m)(α)=(max)-1x1||x|~α-Q(2m)(x)|,Q(2m)(x) is the Lagrange interpolation polynomial to |x|~α based on the Chebyshev nodes:x\-j=cosjπ2m+1(j=1,2,…,2m+1). This result is better than the previous result.更多还原