Constant upper bounds on the matrix exponential norm
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Yuri M. Nechepurenko
Abstract
This work is devoted to the constant (time-independent) upper bounds on the function ∥ exp(tA)∥2 where t ⩾ 0 and A is a square matrix whose eigenvalues have negative real parts. Along with some constant upper bounds obtained from known time-dependent exponential upper bounds based on the solutions of Lyapunov equations, a new constant upper bound is proposed that has significant advantages. A detailed comparison of all these constant upper bounds is carried out using 2 × 2 matrices and matrices of medium size from the well-known NEP collection.
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funding: The work was supported by the Moscow Center of Fundamental and Applied Mathematics (Agreement 075-15-2019-1624 with the Ministry of Education and Science of the Russian Federation).
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Articles in the same Issue
- Frontmatter
- Transfer matrices and solution of the problem of stochastic dynamics of aerosol clusters by Monte Carlo method
- Constant upper bounds on the matrix exponential norm
- On the approximation of the diffusion operator in the ionosphere model with conserving the direction of geomagnetic field
- On numerical computation of sensitivity of response functions to system inputs in variational data assimilation problems
- Model reduction in Smoluchowski-type equations
Articles in the same Issue
- Frontmatter
- Transfer matrices and solution of the problem of stochastic dynamics of aerosol clusters by Monte Carlo method
- Constant upper bounds on the matrix exponential norm
- On the approximation of the diffusion operator in the ionosphere model with conserving the direction of geomagnetic field
- On numerical computation of sensitivity of response functions to system inputs in variational data assimilation problems
- Model reduction in Smoluchowski-type equations
