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Fully precomputed window function

One possibility is to precompute all values $ \varphi(\ensuremath{\boldsymbol{x}}_j - \ensuremath{\boldsymbol{n}}^{-1}\odot\ensuremath{\boldsymbol{l}})$ for $ j=0,\hdots,M-1$ and $ \ensuremath{\boldsymbol{l}}\in I_{\ensuremath{\boldsymbol{n}},m} (\ensuremath{\boldsymbol{x}}_j)$ explicitly. Thus, one has to store the large amount of $ (2m+1)^d M$ real numbers but uses no extra floating point operations during the matrix vector multiplication beside the necessary $ (2m+1)^d M$ flops. Furthermore, we store for this method explicitly the row and column for each nonzero entry of the matrix $ \ensuremath{\boldsymbol{B}}$ . This method, included by the flag PRE_FULL_PSI, is the fastest procedure but can only be used if enough main memory is available.



Jens Keiner 2006-11-20