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MinhNguyen 
Parameter identification is usually encountered in engineering. Some types of problems are listed below. Curve fitting. This is a simple problem when we only have to find the relation between two sets of data: $x$ and $y$. The most common example would be “linear regression”, such that we assume a linear relation: $y = ax … Read more
The Routing vehicle problem (RVP) can be considered as a generalization of the Traveling salesperson problem (TSP). It short, the objective is to find the optimal routes for multiple vehicles to visit a set of locations. The objective is to minimize the total cost of multiple trucks (the number of trucks is known beforehand and … Read more
The Gaussian quadrature for a square domain ([-1, 1] x [-1, 1]) can be conducted by a similar manner to 1D integration (see 1D Gaussian quadrature) $\int \limits_{-1}^{1} \int \limits_{-1}^{1} g(\xi,\eta) d\xi\eta \approx \sum_{i=1}^{n} \sum_{j=1}^{n} g(\xi_i, \eta_j) w_i w_j$, where $\xi$ and $\eta$ denotes the coordinate in horizontal and vertical direction, respectively. Theoretically, the number … Read more
Integration on any straight line of length $L$ can be transformed into integration on the interval [-1, 1] by a simple transformation $\int_{z_{1}}^{z_{2}} f(z) dz = \int \limits_{-1}^{1} \frac{L}{2} f(\xi) d\xi$ Note that the equation for transformation reads $z = \frac{z_2 – z_1}{2} \xi + \frac{z_1 + z_2}{2}$ The integration on interval [-1,1] can be … Read more