| In this thesis we explore the use of the adjoint method for sensitivity analysis and for condition and error estimation applied to three computational models: the solution of linear systems, matrix equations, and ordinary differential equation (ODE) initial value problems. The thesis has two parts. In the first part we present the adjoint method for sensitivity analysis of differential-algebraic equation systems (DAEs). We derive the consistent initial values for the adjoint sensitivity system, prove the stability of the adjoint method, and then describe the implementation of the adjoint method in the code DASPKADJOINT. Numerical results are given to show the efficiency of the adjoint sensitivity method for DAEs. In the second part we show how to use the adjoint method in combination with the small-sample statistical method to estimate the condition and the error of a model. We apply this method to three computational models, giving a detailed discussion and numerical results for each model. |
