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CHAPTER ONE The Riccati Equation
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algorithm analysis analytic application of quasilinearization approach approximation techniques Bellman boundary conditions calculation characteristic value coefficients consider convex DAUX denote differential approximation differential inequalities dipole discussion dynamic programming establish Euler equation existence and uniqueness fashion functional equations given Green's function Hence initial approximation initial condition initial values integration interval Invariant Imbedding INVERSE PROBLEM iteration Kagiwada Kalaba linear algebraic linear algebraic equations linear differential equation linear equation linear systems lower bound Math mathematical matrix method minimum Monotone Convergence Nonlinear Differential Equations nonnegativity numerical solution observation obtain optimal ordinary differential equations parameters partial differential equations Picard Princeton Proc procedure quadratic convergence quasilinearization quasilinearization technique RAND Corporation recurrence relation Riccati equation satisfies sequence of approximations simple solution of linear solve storage SUBROUTINE successive approximations tangent theorem tion two-point boundary-value problems un(x un+1 value problem variable variational problem vector vector-matrix write xn+1 yields