Efficient storage scheme for n-dimensional sparse array: GCRS/GCCS

Shaikh, Abu Hanif; Hasan, K. M. Azharul

doi:10.1109/hpcsim.2015.7237032

Cited by 12 publications

(2 citation statements)

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“…Leveraging the sparse and block Kronecker structure allows us to bring down this computation/memory footprint by two to three orders of magnitude approximately, i.e., GFlops/GBytes of computation/memory required. Upon calculation of the matrix H, we solve (45) by means of conjugate gradient descent. Our implementation leverages the routine cg() from Scipy's module scipy.sparse.linalg [57], which is compatible with sparse matrices.…”

Section: Numerical Estimation Proceduresmentioning

confidence: 99%

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Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Caponera

Fageot

Simeoni

et al. 2022

Electron. J. Statist.

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We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distributed collection of spherical random fields is sampled at a few random directions, possibly subject to measurement error. The collection of random fields could be i.i.d. or serially dependent. Though similar setups have already been explored for random functions defined on the unit interval, the nonparametric estimators proposed in the literature often rely on local polynomials, which do not readily extend to the (product) spherical setting. We therefore formulate our estimation procedure as a variational problem involving a generalized Tikhonov regularization term. The latter favours smooth covariance/autocovariance functions, where the smoothness is specified by means of suitable Sobolev-like pseudo-differential operators. Using the machinery of reproducing kernel Hilbert spaces, we establish representer theorems that fully characterize the form of our estimators. We determine their uniform rates of convergence as the number of random fields diverges, both for the dense (increasing number of spatial samples) and sparse (bounded number of spatial samples) regimes. We moreover demonstrate the computational feasibility and practical merits of our estimation procedure in a simulation setting, assuming a fixed number of samples per random field. Our numerical estimation procedure leverages the sparsity and second-order Kronecker structure of our setup to reduce the computational and memory requirements by approximately three orders of magnitude compared to a naive implementation would require.

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Section: Numerical Estimation Proceduresmentioning

confidence: 99%

“…Our implementation leverages the routine cg() from Scipy's module scipy.sparse.linalg [57], which is compatible with sparse matrices. For the simulation setup under consideration, solving (45) numerically took on the order of a few dozen seconds.…”

Section: Numerical Estimation Proceduresmentioning

confidence: 99%