Optimally scaled and optimally conditioned vandermonde and Vandermonde-like matrices

DOI10.1007/s10543-010-0293-1zbMath1214.65021OpenAlexW2011138697MaRDI QIDQ533705

Walter Gautschi

Publication date: 4 May 2011

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-010-0293-1

zbMATH Keywords

numerical examplessingular value decompositioncondition numbersVandermonde matricesoptimal scalingill-conditioned matricesoptimal conditioningVandermonde-Jacobi matrices

Mathematics Subject Classification ID

Numerical computation of matrix norms, conditioning, scaling (65F35) Conditioning of matrices (15A12) Preconditioners for iterative methods (65F08)

Related Items

Fast factorization of rectangular Vandermonde matrices with Chebyshev nodes ⋮ Optimally scaled vector regularization method to solve ill-posed linear problems ⋮ The pre/post equilibrated conditioning methods to solve Cauchy problems ⋮ Stable extrapolation of analytic functions ⋮ Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units ⋮ Optimally Conditioned Vandermonde-Like Matrices ⋮ An equilibrated method of fundamental solutions to choose the best source points for the Laplace equation ⋮ OCVdM ⋮ Data Driven Koopman Spectral Analysis in Vandermonde--Cauchy Form via the DFT: Numerical Method and Theoretical Insights ⋮ Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations. I: Basics and ansatz function choices

Uses Software

• OPQ

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The condition of Vandermonde-like matrices involving orthogonal polynomials
• Error analysis of the Björck-Pereyra algorithms for solving Vandermonde systems
• Lower bounds for the condition number of Vandermonde matrices
• Norm estimates for inverses of Vandermonde matrices
• Optimally conditioned Vandermonde matrices
• The condition number of real Vandermonde, Krylov and positive definite Hankel matrices
• Condition numbers and equilibration of matrices
• Fast Solution of Vandermonde-Like Systems Involving Orthogonal Polynomials