The Riccati Equation

  • Richard E. Bellman
  • Robert S. Roth
Part of the Mathematics and Its Applications book series (MAIA, volume 26)


In this chapter we wish to apply approximation techniques to the study of one of the fundamental equations of mathematical analysis, the first order nonlinear ordinary differential equation.


Riccati Equation Linear Differential Equation Differential Inequality High Order Approximation Positive Definite Matrice 
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Bibliography and Comments

  1. Bellman, R,:1970, Methods of Nonlinear Analysis, vol I & II, Academic Press, N.Y.Google Scholar
  2. Bellman, R.:1978, “Quasilinearization and the Matrix Riccati Equation”, JMAA, 64,1, 106–113Google Scholar
  3. Bellman, R. and R. Kalaba,:1965, Quasi-linear ization and Nonlinear Boundary Value Problems, American Elsevier, N.Y.Google Scholar
  4. Bellman, R, and R. Vasudevan:1967, “Upper and Lower Bounds for the Solution of the Matrix Riccati Equation”, JMAA, 17, 373–379zbMATHGoogle Scholar

Copyright information

© D Reidel Publishing Company 1986

Authors and Affiliations

  • Richard E. Bellman
    • 1
    • 2
  • Robert S. Roth
    • 3
  1. 1.Department of Electrical EngineeringUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Center for Applied MathematicsThe University of GeorgiaAthensUSA
  3. 3.BostonUSA

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