Fast QR factorization of Vandermonde matrices

DOI10.1016/0024-3795(89)90652-6zbMath0687.65025OpenAlexW1972706155MaRDI QIDQ1263232

Cèdric J. Demeure

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1016/0024-3795(89)90652-6

zbMATH Keywords

complexityCholesky factorizationfast algorithmnormal equationsVandermonde matrixQR factorizationleast squares solutionexponential mode fittingHilbert type matrixProny's two step algorithm

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Iterative numerical methods for linear systems (65F10) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items (10)

Explicit solution of the polynomial least-squares approximation problem on Chebyshev extrema nodes ⋮ Bernstein Bézoutians and application to intersection problems ⋮ Complexity reduction of least squares problems involving special Vandermonde matrices ⋮ Deterministic sparse FFT for \(M\)-sparse vectors ⋮ The Gramian expression of a Vandermonde matrix on symmetric points ⋮ Rectangular Vandermonde matrices on Chebyshev nodes ⋮ Deterministic sparse sublinear FFT with improved numerical stability ⋮ On the normal matrix of the polynomial LS problem over the Chebyshev points ⋮ Symbiosis between linear algebra and optimization ⋮ \textsc{mxpfit}: a library for finding optimal multi-exponential approximations

Cites Work

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• Linear complexity parallel algorithms for linear systems of equations with recursive structure
• Algebraic methods for Toeplitz-like matrices and operators
• Efficient solution of linear systems of equations with recursive structure
• A General Orthogonalization Technique with Applications to Time Series Analysis and Signal Processing

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