This PhD thesis consists of a summary and seven papers, where various applications of auto-validated computations are studied.In the first paper we describe a rigorous method to determine unknown parameters in a system of ordinary differential equations from measured data with known
Stochastic approximation is one of the oldest approaches for solving stochastic optimization problems. In the first part of the dissertation, we study the convergence and asymptotic normality of a generalized form of stochastic approximation algorithm with deterministic perturbation sequences. Both one-simulation and
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