Complexity reduction of least squares problems involving special Vandermonde matrices (Q675689)

The author develops a new QRD factorization of a rectangular Vandermonde matrix of a special point distribution, including the symmetric case, based on a \(K\)-dimensional block decomposition of the matrix and some properties of the Kronecker product. The computational reduction factor with respect to any QR method is \(K^2\), in the general case, and 4 in the symmetric case. Using this factorization, new formulas are derived for the least squares system solution, whose implementation produces an algorithm of reduced computational cost and computer storage. Finally the perturbation bounds of this new factorization are derived.