Projects-NM-HCMUT-2010-large

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

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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?...
View Full Document

{[ snackBarMessage ]}

### Page1 / 10

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

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online