In the paper, a result of Walsh and Sharma on least square convergence of Lagrange interpolation polynomials based on the n-th roots of unity is extended to Lagrange interpolation on the sets obtained by projecting ve...In the paper, a result of Walsh and Sharma on least square convergence of Lagrange interpolation polynomials based on the n-th roots of unity is extended to Lagrange interpolation on the sets obtained by projecting vertically the zeros of (1-x)2=P (a,β) n(x),a>0,β>0,(1-x)P(a,β) n(x),a>0,β>-1,(1+x)P P(a,β) n(x),a>-1,β0 and P(a,β) n(x),a>-1,β>-1, respectively, onto the unit circle, where P(a,β) n(x),a>-1,β>-1, stands for the n-th Jacobi polynomial. Moreover, a result of Saff and Walsh is also extended.展开更多
The object of this paper is to show regularity of(0,1,...,r-2,r) interpolation on the set obtained by projecting vertically the zeros of (1-x2)pn(x)(λ≥1/2)onto the unit circle,where Pn(x)stands for the nth ultrasphe...The object of this paper is to show regularity of(0,1,...,r-2,r) interpolation on the set obtained by projecting vertically the zeros of (1-x2)pn(x)(λ≥1/2)onto the unit circle,where Pn(x)stands for the nth ultraspherical polynomial.展开更多
基金NSFC under grant1 0 0 71 0 3 9and by Education Committee of Jiangsu Province under grant0 0 KJB1 1 0 0 0 5 .
文摘In the paper, a result of Walsh and Sharma on least square convergence of Lagrange interpolation polynomials based on the n-th roots of unity is extended to Lagrange interpolation on the sets obtained by projecting vertically the zeros of (1-x)2=P (a,β) n(x),a>0,β>0,(1-x)P(a,β) n(x),a>0,β>-1,(1+x)P P(a,β) n(x),a>-1,β0 and P(a,β) n(x),a>-1,β>-1, respectively, onto the unit circle, where P(a,β) n(x),a>-1,β>-1, stands for the n-th Jacobi polynomial. Moreover, a result of Saff and Walsh is also extended.
文摘The object of this paper is to show regularity of(0,1,...,r-2,r) interpolation on the set obtained by projecting vertically the zeros of (1-x2)pn(x)(λ≥1/2)onto the unit circle,where Pn(x)stands for the nth ultraspherical polynomial.
