Extension and further development of the differential calculus for matrix norms with applications.

DOI10.1016/S0377-0427(03)00385-6zbMath1042.65051MaRDI QIDQ1398715

Ludwig Kohaupt

Publication date: 7 August 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

fundamental matrixmatrix functionslogarithmic derivativebest upper bounddifferential calculus for matrix norms

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (5)

Solution of the matrix eigenvalue problem \(VA+A^{*}V=\mu V\) with applications to the study of free linear dynamical systems ⋮ New upper bounds for excited vibration systems with applications of the differential calculus of norms ⋮ Two-sided bounds on some output-related quantities in linear stochastically excited vibration systems with application of the differential calculus of norms ⋮ Differential calculus for the matrix norms |·|₁ and |·|_∞ with applications to asymptotic bounds for periodic linear systems ⋮ Two-sided bounds for the asymptotic behaviour of free nonlinear vibration systems with application of the differential calculus of norms

Cites Work

• A relation between the weighted logarithmic norm of a matrix and the Lyapunov equation
• Differential calculus for \(p\)-norms of complex-valued vector functions with applications
• Logarithmic derivative of a square matrix
• Minimization of norms and logarithmic norms by diagonal similarities
• A further remark on the logarithmic derivatives of a square matrix
• How Close Can the Logarithmic Norm of a Matrix Pencil Come to the Spectral Abscissa?
• Solving Ordinary Differential Equations I
• On Logarithmic Norms
• Logarithmic Norms for Matrix Pencils
• Second Logarithmic Derivative of a Complex Matrix in the Chebyshev Norm
• Differential calculus for some \(p\)-norms of the fundamental matrix with applications
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