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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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Wavelet calculations.


he present section builds on the techniques presented in the section ( Wavelet analysis ). Our goal is to construct a wavelet basis on a bounded interval with well conditioned $L_{2}$ Gram matrix. The critical importance of such goal will be evident when we consider using wavelets as finite elements and apply such technique to Black equation.




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].

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