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An estimate of Green's function of the problem of bounded solutions in the case of a triangular coefficient

Numerical Analysis 2024-12-20 v1 Numerical Analysis Dynamical Systems Spectral Theory

Abstract

An estimate of Green's function of the bounded solutions problem for the ordinary differential equation x(t)Bx(t)=f(t)x'(t)-Bx(t)=f(t) is proposed. It is assumed that the matrix coefficient BB is triangular. This estimate is a generalization of the estimate of the matrix exponential proved by Ch. F. Van Loan.

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Cite

@article{arxiv.1901.00792,
  title  = {An estimate of Green's function of the problem of bounded solutions in the case of a triangular coefficient},
  author = {V. G. Kurbatov and I. V. Kurbatova},
  journal= {arXiv preprint arXiv:1901.00792},
  year   = {2024}
}

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10 pages