Vandermonde systems on Gauss-Lobatto Chebyshev nodes

⎧Q(1, n − 2) = 2Q(i, n + 1 − i) = (−1) ii = 1, 2, ..., n⎪⎨ Q(1, n − 2j − 2) = −Q(1, n − 2j),j = 1, 2, ..., ⌈ n−42 ⌉Q(i, n + 1 − i − 2j) = −Q(i, n + 3 − i − 2j) − Q(i − 1, n + 2 − i − 2j), i = 2, 3, ..., n;j = 1, 2, ..., j ∗⎪⎩ Q(i,1) = Q(i,1)/2,i = 1, 2, ..., n(32)where⎧⎪⎨j ∗ =⎪⎩⌊ n−i2 ⌋ n even⌈ n−1−i2⌉ n odd4 The Frobenius norm of V n and W nProposition 1 The Frobenius norm of V n is√ n − 1‖V n ‖ F = n +2 + √ 2 (n − 1) Γ ( n + )122n−3 π Γ(n)(33)where Γ(x) is the gamma function [20].Proof.‖V n ‖ 2 F =n∑n∑i=1 s=1[ ( )] s − 1 2i−2cosn − 1 π (34)But9