Vandermonde matrix


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Vandermonde matrix

[′van·dər‚mȯnd ‚mā·triks]
(mathematics)
A matrix in which each entry in the first row is 1, and each entry in the i th row is the corresponding entry in the second row to the (i - 1) power.
References in periodicals archive ?
For example, a possible systematic solution would be the generalization of the Vandermonde matrix to any hyperoperation of rank r.
Denote V(t) as the K x L Vandermonde matrix with klth element given by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where t = {[[tau].
note that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is not 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.
A novel and simple recursive algorithm for inverting Vandermonde matrix and its confluent type is presented.
The underlying matrix is a Vandermonde matrix based on the total-degree product Chebyshev basis of the smallest rectangle containing the compact domain.
m] is a increasing-power mth-order Vandermonde matrix whose size is Ns x (m + 1).
Observe that if w is analytic itself in K, the maximum modulus of the determinant of the weighted Vandermonde matrix (2.
The interpolation problem and the 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 [E.