Perturbation of the matrix sign function

DOI10.1016/0024-3795(95)00522-6zbMath0871.15027OpenAlexW1975132935MaRDI QIDQ5961582

Ji-guang Sun

Publication date: 25 February 1997

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

Full work available at URL: https://doi.org/10.1016/0024-3795(95)00522-6

zbMATH Keywords

condition numberperturbation expansionsJordan decompositionperturbation boundsFréchet derivativesmatrix sign functionSchur decomposition

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Conditioning of matrices (15A12)

Related Items

Perturbation analysis for the sign functions of regular matrix pairs ⋮ The complex step approximation to the Fréchet derivative of a matrix function ⋮ An arithmetic for matrix pencils: theory and new algorithms

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stability radius for structured perturbations and the algebraic Riccati equation
• Perturbation expansions for invariant subspaces
• Inertia characteristics of self-adjoint matrix polynomials
• A computational method for eigenvalues and eigenvectors of a matrix with real eigenvalues
• A hyperbolic tangent identity and the geometry of Padé sign function iterations
• The matrix sign decomposition and its relation to the polar decomposition
• A Bisection Method for Measuring the Distance of a Stable Matrix to the Unstable Matrices
• Linear model reduction and solution of the algebraic Riccati equation by use of the sign function†
• Accelerated convergence of the matrix sign function method of solving Lyapunov, Riccati and other matrix equations
• Error and Perturbation Bounds for Subspaces Associated with Certain Eigenvalue Problems
• Polar Decomposition and Matrix Sign Function Condition Estimates