note that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is not the form of the generalized Vandermonde matrix.
In this step, we will change [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to the form of the generalized Vandermonde matrix.
N]} of distinct elements from K is Lagrange type, since the matrix M is a Vandermonde matrix
, hence nonsingular.
The underlying matrix is a Vandermonde matrix based on the total-degree product Chebyshev basis of the smallest rectangle containing the compact domain.
i,j] denote the generalized Vandermonde matrix for this basis in the points X.
Observe that if w is analytic itself in K, the maximum modulus of the determinant of the weighted Vandermonde matrix (2.
4, we use the standard complex monomial basis to construct the Vandermonde matrix, with two refinement iterations in Algorithm AFP.
The interpolation problem and the Vandermonde matrix
1] N where the numerator matrix N is an m x n Vandermonde matrix
n=21; % number of interpolation points m=1000; x=linspace(-1,1,m); % discrete model of [-1,1] A = gallery('chebvand',n,x); % A is the n by m Vandermonde matrix
% in the Chebyshev polynomial basis b=rand(n,1); % a random rhs y=A\b; % y is the MATLAB solution of Ay=b pp=y~=0; % vector of indices of the non-zero elements of y pts=x(pp) % selects the points from x according to pp
Then the experiments showed that when n [greater than or equal to] 20 it is no longer wise to invert the Vandermonde matrix
matrix exponential, Vandermonde matrix
, fast algorithm, inverse.