Some remarks on matrix norms, condition numbers, and error estimates for linear equations

DOI10.1016/0024-3795(83)90130-1zbMath0654.15018OpenAlexW2009903396MaRDI QIDQ1108352

Gerhard Zielke

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1016/0024-3795(83)90130-1

zbMATH Keywords

error estimatesnormscondition numbers

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items

Perturbation analysis for the operator equation \(Tx=b\) in Banach spaces ⋮ A note on bound for norms of Cauchy–Hankel matrices ⋮ On k-circulant matrices with the Lucas numbers ⋮ On some generalizations of Horadam’s numbers ⋮ On the spectral norms of r-circulant and geometric circulant matrices with the bi-periodic hyper-Horadam sequence ⋮ The spectral norms of geometric circulant matrices with the generalized \(k\)-Horadam numbers ⋮ On \(k\)-circulant matrices involving the Pell-Lucas (and the modified Pell) numbers ⋮ A hybrid sequential sampling strategy for sparse polynomial chaos expansion based on compressive sampling and Bayesian experimental design ⋮ On \(k\)-circulant matrices involving the Pell numbers ⋮ A study of Auchmuty's error estimate ⋮ Moderate Gain Luenberger-Like Observer for Lipschitz Nonlinear Dynamics ⋮ Unnamed Item

Cites Work

• Inertia characteristics of self-adjoint matrix polynomials
• Report on test matrices for generalized inverses
• Computable Accurate Upper and Lower Error Bounds for Approximate Solutions of Linear Algebraic Systems
• Extensions and Applications of the Householder Algorithm for Solving Linear Least Squares Problems
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item