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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) Airpollution prediction modelling . Use MATLABb to predict airpollution with a timeseries 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 kth day, and • V [ k ]: predicted average wind speed in the kth 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 airpollution? 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 6by2 matrix E = [ ones ( size ( t )) exp ( t )] a) Can you mathematically solve the problem?...
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 Spring '08
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 Numerical Analysis, Data Structures, Polynomial interpolation, state equation

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