Rectangular Vandermonde matrices on Chebyshev nodes

DOI10.1016/S0024-3795(01)00355-XzbMath0992.15023OpenAlexW1991830491MaRDI QIDQ5955645

Nicola Salerno, Alfredo Eisinberg, Giuseppe Franzè

Publication date: 16 September 2002

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0024-3795(01)00355-x

zbMATH Keywords

combinatorial identitiesnumerical experimentscondition numberrectangular Vandermonde matrixfactorizationsroots of Chebyshev polynomials

Mathematics Subject Classification ID

Factorization of matrices (15A23) Theory of matrix inversion and generalized inverses (15A09) Combinatorics in computer science (68R05) Least squares and related methods for stochastic control systems (93E24) Hermitian, skew-Hermitian, and related matrices (15B57) Numerical computation of matrix norms, conditioning, scaling (65F35) Conditioning of matrices (15A12)

Related Items (6)

Stable super-resolution limit and smallest singular value of restricted Fourier matrices ⋮ Explicit solution of the polynomial least-squares approximation problem on Chebyshev extrema nodes ⋮ Fast factorization of rectangular Vandermonde matrices with Chebyshev nodes ⋮ Optimally Conditioned Vandermonde-Like Matrices ⋮ On the normal matrix of the polynomial LS problem over the Chebyshev points ⋮ Vandermonde systems on Gauss-Lobatto Chebyshev nodes

Uses Software

• Mathematica
• Matlab

Cites Work

• The condition of Vandermonde-like matrices involving orthogonal polynomials
• Lower bounds for the condition number of Vandermonde matrices
• Vandermonde matrices on Chebyshev points
• Norm estimates for inverses of Vandermonde matrices
• Fast QR factorization of Vandermonde matrices
• Vandermonde matrices on integer nodes
• On the Stationary Values of a Second-Degree Polynomial on the Unit Sphere
• Vandermonde matrices on integer nodes: The rectangular case
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