Projects-NM-HCMUT-2010-large - Projects& Group...

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Unformatted text preview: Projects & Group Discussions for Numerical Methods Man V. M. Nguyen Ph.D. in Statistics September 6, 2010 1 Suggested Topics/ Models for NM presentation ======= Chapters 1 and 2 ========= 1. (Suggested Project) Air-pollution prediction modelling . Use MATLABb to predict air-pollution with a time-series recursive model describing the atmospheric concentration of SO 2 . Recall: let Y [ k + 1] be the atmospheric concentration of SO 2 at time point k + 1 in HCMC, then we can write: Y [ k + 1] = a · Y [ k ] + b ( T [ k + 1] + c ) 2 + d V [ k + 1] + e , where • a, b, c, d, e : scalars, usually real numbers • T [ k ]: predicted average temp. in the k-th day, and • V [ k ]: predicted average wind speed in the k-th day. a) Set a, b, c, d, e be specific values and suggest concrete formulae of T [ k ] and V [ k ]. b) Compute explicit formula of Y [ k ] using a). b) Visualize Y [ k ] in 15 consecutive days. d) (*) How do you believe that your model is best in explaining or predicting the air-pollution? 2. (Suggested Project) Develop a reasonable model of Water resistance of vessels problem- use multivariate polynomial interpolation to carry out completely the solution of this case study- write a small program implementing your solution 2 3. (Chapter 1 & 2) Overdetermined systems and least squares . Overdetermined systems of simultaneous linear equations are often encountered in various kinds of curve fitting to experimental data. A quantity y is measured at several different values of time, t (in minute) t = [0 . 3 , . 8 , 1 . 1 , 1 . 6 , 2 . 3 , 3]; y = [82 , 72 , 63 , 60 , 55 , 50] . Aim : Try modeling the data with a decaying exponential function : y = c 1 + c 2 e- t The preceding equation says that the vector y should be approximated by a linear combination of two other vectors, one the constant vector containing all ones and the other the vector with components e- t . The unknown coefficients, c 1 and c 2 , can be computed by doing a least squares fit, which minimizes the sum of the squares of the deviations of the data from the model. There are six equations in two unknowns, represented by the 6-by-2 matrix E = [ ones ( size ( t )) exp (- t )] a) Can you mathematically solve the problem?...
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Projects-NM-HCMUT-2010-large - Projects& Group...

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