Quantitative Analysis
Parallel Processing
Numerical Analysis
C++ Multithreading
Python for Excel
Python Utilities

I. Wavelet calculations.
1. Calculation of scaling filters.
2. Calculation of scaling functions.
3. Calculation of wavelets.
4. Convergence of cascade procedure.
5. Direct verification of wavelet properties.
6. Adapting scaling function to the interval [0,1].
7. Adapting wavelets to the interval [0,1].
II. Calculation of approximation spaces in one dimension.
III. Calculation of approximation spaces in one dimension II.
IV. One dimensional problems.
V. Stochastic optimization in one dimension.
VI. Scalar product in N-dimensions.
VII. Wavelet transform of payoff function in N-dimensions.
VIII. Solving N-dimensional PDEs.
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Calculation of scaling filters.

he procedure for calculation of biorthogonal GMRA filters MATH and MATH was described in the section ( Symmetric biorthogonal wavelets ). The Mathematica scripts are located in the files "OTSProjects\mathematica\wavelets\symmetric.txt" and "OTSProjects\mathematica\wavelets\io.txt".

Running those scripts with several values of the parameter n generates the results files "sym1_<n>.txt" and "sym2_<n>.txt" in the directory "OTSProjects\mathematica\data". These files contain the scaling filters MATH and MATH .

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Copyright 2007