A matrix function useful in the estimation of linear continuous-time models

• Autores: Heinz Neudecker
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 30, Nº. 1, 2006, págs. 85-90
• Idioma: inglés
• Títulos paralelos:
  • Una función matricial útil en la estimación de modelos lineales continuos.
• Enlaces
  • Texto completo (pdf)
• Resumen

  • In a recent publication Chen & Zadrozny (2001) derive some equations for efficiently computing eA and ¿Þ eA, its derivative. They employ an expression due to Bellman (1960), Snider (1964) and Wilcox (1967) for the differential deA and a method due to Van Loan (1978) to find the derivative ¿Þ eA. The present note gives a) a short derivation of ¿Þ eA by way of the Bellman-Snider-Wilcox result, b) a shorter derivation without using it. In both approaches there is no need for Van Loan¿fs method.

• Referencias bibliográficas
  • Bellman, R. (1960). Introduction to Matrix Analysis. McGraw-Hill, New York.
  • Chen, B. and Zadrozny, P. A. (2001). Analytic derivatives of the matrix exponential for estimation of linear continuous-time models. Journal...
  • Neudecker, H. (1971). On a theorem of Snider and Wilcox. METU Journal of Pure and Applied Sciences, 4, 217-220.
  • Snider, R. F. (1964). Perturbation variation methods for a quantum Boltzmann equation. Journal of Mathematical Physics, 5, 1580-1587.
  • Van Loan, C. F. (1978). Computing integrals involving the matrix exponential. IEEE Transactions on Automatic Control, 23, 395-404.
  • Wilcox, R. M. (1967). Exponential operators and parameter differentiation in quantum physics. Journal of Mathematical Physics, 8, 962-982.