An Efficient Parallel Algorithm to Solve Block?Toeplitz Systems

Alonso, Pedro; Badía, Jordi; Vidal, Antonio M.

doi:10.1007/s11227-005-0182-6

Cited by 12 publications

(3 citation statements)

References 30 publications

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“…1, by using an algorithm based on fast block Toeplitz solvers [2]. In addition, one may also use A (N,J) ω (0) to build a banded limited preconditioner by dropping some off-diagonal blocks T n for solving (62), then generalizing P = (A (0,J)…”

Section: Finite Element Approximationmentioning

confidence: 99%

A MultiHarmonic Finite Element Method for Scattering Problems with Small-Amplitude Boundary Deformations

Gasperini¹,

Beise²,

Schroeder³

et al. 2022

SIAM J. Sci. Comput.

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Section: Finite Element Approximationmentioning

confidence: 99%

A MultiHarmonic Finite Element Method for Scattering Problems with Small-Amplitude Boundary Deformations

Gasperini¹,

Beise²,

Schroeder³

et al. 2022

SIAM J. Sci. Comput.

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“…Since we ideally would like to learn the unknown function f across X , we instead consider a regular equidistant grid of inducing points Z covering the region of interest. For stationary kernels, this results in Block-Toeplitz-Toeplitz-Block (BTTB)-structure, for which a small number of specialized algorithms exist [ABV05]. We will see in the following that, even for non-stationary GIM kernels, it is possible to reduce the computational effort through the choice of inducing points.…”

Section: Sparse Gpsmentioning

confidence: 99%

Learning ODE Models with Qualitative Structure Using Gaussian Processes

Ridderbusch,

Offen,

Ober-Blöbaum

et al. 2020

Preprint

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Recent advances in learning techniques have enabled the modelling of dynamical systems for scientific and engineering applications directly from data. However, in many contexts, explicit data collection is expensive and learning algorithms must be dataefficient to be feasible. This suggests using additional qualitative information about the system, which is often available from prior experiments or domain knowledge. In this paper, we propose an approach to learning the vector field of differential equations using sparse Gaussian Processes that allows us to combine data and additional structural information, like Lie Group symmetries and fixed points, as well as known input transformations. We show that this combination improves extrapolation performance and longterm behaviour significantly, while also reducing the computational cost.

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“…Parallel Schur-type algorithms can be found, i.e., in [22] where the least squares problem is solved with a refinement step to improve the accuracy of the solution. Also, the block-Toeplitz case is a practical study in [23,24].…”

Section: Introductionmentioning

confidence: 99%

A multilevel parallel algorithm to solve symmetric Toeplitz linear systems

2007

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This paper presents a parallel algorithm to solve a structured linear system with a symmetric-Toeplitz matrix. Our main result concerns the use of a combination of shared and distributed memory programming tools to obtain a multilevel algorithm that exploits the actual different hierarchical levels of memory and computational units present in parallel architectures. This gives, as a result, a so-called parallel hybrid algorithm that is able to exploit each of these different configurations. Our approach has been done not only by means of combining standard implementation tools like OpenMP and MPI, but performing the appropriate mathematical derivation that allows this derivation. The experimental results over different representations of available parallel hardware configurations show the usefulness of our proposal.

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An Efficient Parallel Algorithm to Solve Block?Toeplitz Systems

Cited by 12 publications

References 30 publications

A MultiHarmonic Finite Element Method for Scattering Problems with Small-Amplitude Boundary Deformations

A MultiHarmonic Finite Element Method for Scattering Problems with Small-Amplitude Boundary Deformations

Learning ODE Models with Qualitative Structure Using Gaussian Processes

A multilevel parallel algorithm to solve symmetric Toeplitz linear systems

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