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...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.展开更多
In this work, the well-known problem put forward by S N Bernstein in 1930 is studied in a deep step. An operator is constructed by revising double interpolation nodes. It is proved that the operator converges to arbit...In this work, the well-known problem put forward by S N Bernstein in 1930 is studied in a deep step. An operator is constructed by revising double interpolation nodes. It is proved that the operator converges to arbitrary continuous functions uniformly and the convergence order is the best.展开更多
文摘研究插值多项式对|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.
基金Foundation item： Supported by the National Natural Science Foundation of China（10626045）
文摘In this work, the well-known problem put forward by S N Bernstein in 1930 is studied in a deep step. An operator is constructed by revising double interpolation nodes. It is proved that the operator converges to arbitrary continuous functions uniformly and the convergence order is the best.
