Cholesky factorization

Higham, Nicholas J.

doi:10.1002/wics.18

Cited by 126 publications

(75 citation statements)

References 9 publications

(9 reference statements)

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“…However, in contrast to the problems described in [3], whereas the aggregation and disaggregation matrices were dependent only on a group of sources, and thus only on few h i , here, they are still dependent on all independent RVs ξ. Besides the aforementioned curse of dimensionality in calculating PCE projections (7), this also entails an unacceptably long solution time of (8). Indeed, since the aggregation and the disaggregation matrices are dependent on all independent RVs, their PCE coefficients are all nonzero and the complexity does not scale linearly with the number of polynomials K as in [3], but with the total number of γ klm .…”

Section: Cholesky-based Sgm-mlfmmmentioning

confidence: 99%

A Cholesky-Based SGM-MLFMM for Stochastic Full-Wave Problems Described by Correlated Random Variables

Zubac

Daniel

Zutter

et al. 2017

Antennas Wirel. Propag. Lett.

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Abstract-In this letter, the Multilevel Fast Multipole Method (MLFMM) is combined with the Polynomial Chaos Expansion (PCE) based Stochastic Galerkin Method (SGM) to stochastically model scatterers with geometrical variations that need to be described by a set of correlated random variables (RVs). It is demonstrated how Cholesky decomposition is the appropriate choice for the RVs transformation, leading to an efficient SGM-MLFMM algorithm. The novel method is applied to the uncertainty quantification (UQ) of the currents induced on a rough surface, being a classic example of a scatterer described by means of correlated RVs, and the results clearly demonstrate its superiority compared to non-intrusive PCE methods and to the standard Monte Carlo (MC) method.

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Section: Cholesky-based Sgm-mlfmmmentioning

confidence: 99%

A Cholesky-Based SGM-MLFMM for Stochastic Full-Wave Problems Described by Correlated Random Variables

Zubac

Daniel

Zutter

et al. 2017

Antennas Wirel. Propag. Lett.

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“…The Cholesky factorization of a n×n matrix has a complexity in term of floating point operation of n 3 /3 that is half of the LU one (2n 3 /3), and is numerically more stable [9], [10]. This algorithm is naturally in-place as every input element is accessed only once and before writing the associated element of the output: L and A can be the same storage.…”

Section: A Cholesky Factorizationmentioning

confidence: 99%

Batched Cholesky factorization for tiny matrices

Lemaître

Lacassagne

2016

2016 Conference on Design and Architectures for Signal and Image Processing (DASIP)

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Abstract-Many linear algebra libraries, such as the Intel MKL, Magma or Eigen, provide fast Cholesky factorization. These libraries are suited for big matrices but perform slowly on small ones. Even though State-of-the-Art studies begin to take an interest in small matrices, they usually feature a few hundreds rows. Fields like Computer Vision or High Energy Physics use tiny matrices. In this paper we show that it is possible to speedup the Cholesky factorization for tiny matrices by grouping them in batches and using highly specialized code. We provide High Level Transformations that accelerate the factorization for current Intel SIMD architectures (SSE, AVX2, KNC, AVX512). We achieve with these transformations combined with SIMD a speedup from 13 to 31 for the whole resolution compared to the naive code on a single core AVX2 machine and a speedup from 15 to 33 with multithreading compared to the multithreaded naive code.

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“…Superscript T indicates matrix transposition. Observe that (4) and (5) use a variant of the Cholesky factorization, defined in [7] as:…”

Section: Channel Modelingmentioning

confidence: 99%

Channel characteristics analysis of the dual circular polarized land mobile satellite MIMO radio channel

Ekpe

Brown

Evans

2011

2011 IEEE-APS Topical Conference on Antennas and Propagation in Wireless Communications

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− − − − This paper analyses the characteristics of the dual circular polarized land mobile satellite MIMO radio channel using measured and modeled channel data. To describe the small scale fading observed in the measured channel, the model makes use of three parameters, which respectively represent the mean LOS, specular reflected and diffuse multipath signals. The model is validated by comparing the CDF plots of the received signal power and eigenvalues with that of the measured channel. Furthermore, the effects of channel correlation on the capacities of equal power allocation MIMO and dual circular polarization multiplexing (DCPM) is investigated. It is found that only the capacity of the LOS-friendly DCPM is negatively affected by a reduction in channel correlation.

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Cholesky factorization

Cited by 126 publications

References 9 publications

A Cholesky-Based SGM-MLFMM for Stochastic Full-Wave Problems Described by Correlated Random Variables

A Cholesky-Based SGM-MLFMM for Stochastic Full-Wave Problems Described by Correlated Random Variables

Batched Cholesky factorization for tiny matrices

Channel characteristics analysis of the dual circular polarized land mobile satellite MIMO radio channel

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