Differential calculus for \(p\)-norms of complex-valued vector functions with applications

DOI10.1016/S0377-0427(01)00594-5zbMath1055.65057MaRDI QIDQ1612417

Ludwig Kohaupt

Publication date: 22 August 2002

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

zbMATH Keywords

error boundsvibration problemright derivativedifferential calculus for vector normsnorm of a vector function

Mathematics Subject Classification ID

Vector and tensor algebra, theory of invariants (15A72) Nonlinear ordinary differential equations and systems (34A34) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical computation of matrix norms, conditioning, scaling (65F35) Error bounds for numerical methods for ordinary differential equations (65L70) Systems arising from the discretization of structural vibration problems (70J50)

Related Items (11)

Trigonometric spline and spectral bounds for the solution of linear time-periodic systems ⋮ Extension and further development of the differential calculus for matrix norms with applications. ⋮ New upper bounds for free linear and nonlinear vibration systems with applications of the differential calculus of norms ⋮ Observations on evolutionary models with (or without) time lag, and on problematical paradigms ⋮ Solution of the matrix eigenvalue problem \(VA+A^{*}V=\mu V\) with applications to the study of free linear dynamical systems ⋮ Illustration of the logarithmic derivatives by examples suitable for classroom teaching ⋮ 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 ⋮ Two-sided bounds on the mean vector and covariance matrix 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

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• 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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