Course aims:

After going through the course, students will acquire skills in using different interpolation methods using MATLAB software in achieving specific problems of geodesy.
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Course Entry Requirements:

N/A

Course contents:

1. Least squares functions approximation 2. Least squares failure 3. Polynomials and matching data in MATLAB 4. Polynomial interpolation 5. Lagrange, Hermite interpolation 6. Calculation of polynomial interpolation efficient 7. Aitken type methods 8. Spline interpolation. Linear spline, Cubic spline interpolation. 9. uniform approximation, Bernstein polynomials 10. Applications in MATLAB: 1D interpolation, interpolation by least squares, interpolation Hermite. Using functions: interp1, splines, pchip 11. Applications in MATLAB: 2D and 3D interpolation. Using functions: interp2, interp3 12. Applications in MATLAB: 2D and 3D interpolation. Using functions: interpn, ndgrid 13. Applications in MATLAB: 2D and 3D interpolation. Using functions: meshgrid, griddata

Teaching methods:

Lecture, discussion, exemplification.

Learning outcomes:

In order to obtain credits for this discipline the students have to: - Know the basics on the approximation by least squares, linear interpolation; - Can determine the interpolation error expression; - Can achieve concrete interpolation problem 1D, 2D and 3D using MATLAB - Form their skills to plot different surfaces processed using MATLAB specific functions, such as: interp2, interp3, interpn

Learning outcomes verification and assessment criteria:

Final evaluation – 50%; continuous assessment – 50%.

Recommended reading:

A. Bjork, Numerical Methods for Least Square Problem, SIAM, 196,
Steven Chapra, Applied Numerical Methods With MATLAB: for Engineers & Scientists, 3rd Edition, McGraw-Hill Science, 2011,
William Palm III, Introduction to MATLAB for Engineers, McGraw-Hill Science, 2010,