Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Logarithmic Norms for Matrix Pencils
SIAM Journal on Matrix Analysis and Applications
Second Logarithmic Derivative of a Complex Matrix in the Chebyshev Norm
SIAM Journal on Matrix Analysis and Applications
Differential calculus for some p-norms of the fundamental matrix with applications
Journal of Computational and Applied Mathematics
How Close Can the Logarithmic Norm of a Matrix Pencil Come to the Spectral Abscissa?
SIAM Journal on Matrix Analysis and Applications
Extension and further development of the differential calculus for matrix norms with applications
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
International Journal of Computer Mathematics
Phase diagram for norms of the solution vector of dynamical multi-degree-of-freedom systems
AMERICAN-MATH'10 Proceedings of the 2010 American conference on Applied mathematics
Mathematics and Computers in Simulation
| Hi-index | 7.29 |
For complex-valued n-dimensional vector functions t ↦ s(t), supposed to be sufficiently smooth, the differentiability properties of the mapping t ↦ ∥s(t)∥p at every point t = t0 ∈ R+0 := {t ∈ R | t ≥ 0} are investigated, where ∥.∥p is the usual vector norm in Cn resp. Rn for p ∈ [1, ∞]. Moreover, formulae for the first three right derivatives D+k∥s(t)∥p, k = 1, 2, 3 are determined. These formulae are applied to vibration problems by computing the best upper bounds on ∥s(t)∥p in certain classes of bounds. These results cannot be obtained by the methods used so far. The systematic use of the differential calculus for vector norms, as done here for the first time, could lead to major advances also in other branches of mathematics and other sciences.