Fixed-point simulation results are used for the performance measure of inverting matrices using a reconfigurable processing element. Matrices are inverted using the Cholesky decomposition algorithm. The reconfigurable processing element is capable of all required mathematical operations. The fixed-point word length analysis is based on simulations of different condition numbers and different ma...

This paper discusses an efficient parallel implementation of the ensemble Kalman filter based on the modified Cholesky decomposition. The proposed implementation starts with decomposing the domain into sub-domains. In each sub-domain a sparse estimation of the inverse background error covariance matrix is computed via a modified Cholesky decomposition; the estimates are computed concurrently on

We obtain several asymptotic results on the powers of a square matrix associated with SVD, QR decomposition and Cholesky decomposition.

Dense kernel matrices Θ ∈ RN×N obtained from point evaluations of a covariance function G at locations {xi}1≤i≤N arise in statistics, machine learning, and numerical analysis. For covariance functions that are Green’s functions elliptic boundary value problems and approximately equally spaced sampling points, we show how to identify a subset S ⊂ {1, . . . , N} × {1, . . . , N}, with #S = O ( N ...

A method for simultaneous modelling of the Cholesky decomposition of several covariance matrices is presented. We highlight the conceptual and computational advantages of the unconstrained parameterization of the Cholesky decomposition and compare the results with those obtained using the classical spectral (eigenvalue) and variance-correlation decompositions. All these methods amount to decomp...

SUMMARY This article is dedicated to the rapid computation of separable expansions for the approximation of random fields. We consider approaches based on techniques from the approximation of non-local operators on the one hand and based on the pivoted Cholesky decomposition on the other hand. Especially, we provide an a-posteriori error estimate for the pivoted Cholesky decomposition in terms ...

In this paper two ways to compute singular values are presented which use Cholesky decomposition as their basic operation.

We report an error estimate of the multi-dimensional fast Gauss transform (FGT), which is much sharper than that previously reported in the literature. An application to the Karhunen–Loeve decomposition in the three-dimensional physical space is also presented that shows savings of three orders of magnitude in time and memory compared to a direct solver. 2006 Elsevier Inc. All rights reserved.