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Several of the different registration algorithms were developed with a library of robust math kernel functions, and the accuracy of all registration techniques was thoroughly investigated.
At present, the Windows build of CRYSTALS is using Intel®; Math Kernel Library (Intel®; MKL) which offers similar performance to OpenBlas.
Recommendations for utilizing the BLAS libraries other than through the free ATLAS (e.g., through the commercial Sun Performance Library or Intel® Math Kernel Library) are included in the Makefile.
GPU: graphics processing unit; CUDA: compute unified device architecture; MIC: many integrated core; FFT: fast Fourier transform; IFFT: inverse fast Fourier transform; PDB: protein data bank; MKL: math kernel library.
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Let T be the multilinear square operator, respectively with certain smooth kernels and non-smooth kernels defined in (Xue and Yan in J. Math. Anal. Appl. 422 1342-1362, 2015) and (Hormozi et al. in arXiv preprint, 2015), and let (T^) be its corresponding maximal operator.
The use of fast math and sm_20 has a significant effect on the kernel times.
Inahama, H. Kawabi, Large deviations for heat kernel measures on loop spaces via rough paths, J. London Math.
As an application of an inequality for modified Poisson kernel obtained by Qiao and Deng (Bull. Malays. Math. Sci. Soc. (2) 36(201311-523, 2013), we give the generalized solution of the Dirichlet problem with arbitrary growth data.
In particular, our results improve B. K. Driver's formula in (1997, J. Math. Pures Appl. (9 76, 703 737) for logarithmic derivatives of the heat kernel measure on a Riemannian manifold.
I must admit that the kernel of these ideas was not mine; rather, a third grade math teacher from Ohio gave me the idea.
For kernel density estimation, the empirical probability distribution implementing the Variable Kernel Method with Gaussian Smoothing of the Apache Commons Math 3.6 API [15] is used.
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