INSTRUCTOR:
Prof. Andrew Knyazev
Office: CU (Dravo Bldg) 644. Phone: (303) 556-8102.
Office hours: by appointment.
WWW: http://math.ucdenver.edu/~aknyazev
IMPORTANT ANNOUNCEMETS:
Please download and use the updated (on December 3) code
interpolating_polynomial.m
where the formulas for the the Chebyshev nodes are corrected. Sorry for possible inconvenience.
The final project covers the following subjects:
Polynomial interpolation,
Minimax approximation,
Least squares approximation.
THE PROJECT DESCRIPTION:
-
SOFTWARE DEVELOPMENT:
- Learn how to call Fortran codes from MATLAB,
and be able to run 501.for.
Check that the Fortran code 501.for produces
results identical to those by the MATLAB code
exchange.m, which has been
developed by a group of students in my
previous Approximation Theory class in 1998.
- Modify the MATLAB code
interpolating_polynomial.m
(provided) so that, in addition to computing interpolating
polynomials on uniform and Chebyshev interpolation nodes,
it also computes the best polynomial least squares
approximation and the best polynomial minimax approximation,
of the corresponding degrees. Use MATLAB's built-in function
polyfit to compute the polynomial least squares approximation.
Use either 501.for or
exchange.m (provided that they
produce identical results) to compute the polynomial
minimax approximation.
- Modify the code
interpolating_polynomial.m
to generate the corresponding movies least_squares.avi and
minimax.avi (in addition to already existing
uniform.avi and chebyshev.avi),
and add the two
new cases to the picture error.png of the approximation error.
-
TESTING:
- Test the code for different functions and interval end points,
trying to find some interesting examples of different behavior
of different approximations. Check the results visually
to make sure the code produces expected polynomials.
-
ANALYSIS:
- Try to explain the results you are getting
for different functions and interval end points.
- Highlight advantages and disadvantages
of different approximation methods used in this project
and illustrate your findings by examples.
-
THE PROJECT REPORT
-
The report should be done electronically on a Web page created specifically for the project.
-
The project report should have links to all movies and pictures generated.
-
The report needs to include a detailed description of the results, including complete descriptions of the movies generated.
-
The project report should include the discussion of testing and
analysis procedures and results.
-
On the due day, please email me the link to your main Web page or directory with the project report and do not change it after that.