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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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Calculation of wavelets.


ith the scaling functions $\phi,\tilde{\phi}$ calculated, we recover the wavelets $\psi,\tilde{\psi}$ (see the section ( Dual wavelets )): MATH MATH The procedure is implemented in the function "wavelets" of the class "FourFunctions" in the file "OTSProjects\python\wavelet\cascade.py".





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