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

I. Wavelet calculations.
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.
1. Two-sided area of integration, positive a.
2. Two-sided area of integration, negative a.
3. Indexing integration domains.
4. Summary. Calculation of scalar product in N dimensions.
5. Indexing integration domains II.
6. Scalar product in N-dimensions. Test case 1.
7. Scalar product in N-dimensions. Test case 2.
8. Scalar product in N-dimensions. Test case 3.
9. Implementation of scalar product in N-dimensions.
VII. Wavelet transform of payoff function in N-dimensions.
VIII. Solving N-dimensional PDEs.
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Indexing integration domains.

ood performance of a Cuda-based implementation needs grouping of alike operations to threads within the same kernel call. Hence, we need to identify the subdomains MATH that include the boundary $B(a,c)$ and we need to establish a 1-to-1 mapping between these domains and a one-dimensional index. To establish such mapping we iterate though all relevant $\left( n-1\right) $ -dimensional subdomains MATH For each MATH we find the complement MATH as follows. Let MATH be the set of vertices of the subdomain MATH . For each $v^{s}$ we find an integer $k_{s}$ such that MATH or MATH Then MATH covers part of the boundary MATH .

There is no need to calculate $k_{s}$ for every $s$ . Indeed, MATH thus a vertex $v^{s}$ of a subdomain MATH is given by MATH Hence MATH MATH

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Copyright 2007