CGLS-GCV: a hybrid algorithm for low-rank-deficient problems
Applied Numerical Mathematics - Special issue: 2nd international workshop on numerical linear algebra, numerical methods for partial differential equations and optimization
Analytically tractable case of fuzzy c-means clustering
Pattern Recognition
Symbolic-numeric sparse interpolation of multivariate polynomials
Journal of Symbolic Computation
Nonlinear Approximation by Sums of Exponentials and Translates
SIAM Journal on Scientific Computing
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Let WN=WN(z1,z2, . . . z1) be a rectangular Vandermonde matrix of order n × N, $N\geq n,$ with distinct nodes zj in the unit disk and $z_j^{k-1}$ as its (j,k) entry. Matrices of this type often arise in frequency estimation and system identification problems. In this paper, the conditioning of WN is analyzed and bounds for the spectral condition number $\kappa_2(W_N)$ are derived. The bounds depend on n, N, and the separation of the nodes. By analyzing the behavior of the bounds as functions of N, we conclude that these matrices may become well conditioned, provided the nodes are close to the unit circle but not extremely close to each other and provided the number of columns of WN is large enough. The asymptotic behavior of both the conditioning itself and the bounds is analyzed and the theoretical results arising from this analysis verified by numerical examples.