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I. Wavelet calculations.
II. Calculation of approximation spaces in one dimension.
III. Calculation of approximation spaces in one dimension II.
IV. Wavelet basis in N-dimensions.

Numerical Analysis.


n this section we put into use the recipes developed in the section ( Implementation tools II ).

We start with wavelet calculations. More will follow shortly.

We assume that the modules r_com and poly are already installed. See the sections ( Python to R Communicator ) and ( Piecewise polynomials ).



Table of Contents.

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.
1. Calculation of boundary scaling functions.
2. Calculation of boundary wavelets.
3. Testing properties of boundary wavelets and scaling functions.
III. Calculation of approximation spaces in one dimension II.
1. Crudification of piecewise-quadratic representation.
2. Convergence of modified cascade procedure.
3. Calculation of boundary scaling functions II.
IV. Wavelet basis in N-dimensions.
1. Wavelet transform of payoff function in N-dimensions.
A. Separation of variables for payoff function.
B. Scalar product in N-dimensions.
C. Two-sided area of integration, positive a.
D. Calculation of w1 for positive a.
E. Calculation of w2 for positive a.
F. Calculation of w3 for positive a.
G. Two-sided area of integration, negative a.
H. Calculation of w1 for negative a.
I. Calculation of w2 for negative a.
J. Calculation of w3 for negative a.
K. Indexing integration domains.
L. Summary. Calculation of scalar product in N dimensions.
M. Indexing integration domains II.
N. Scalar product in N-dimensions. Test case 1.
O. Scalar product in N-dimensions. Test case 2.
P. Scalar product in N-dimensions. Test case 3.
Q. Implementation of scalar product in N-dimensions.



















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