Computational experience with sequential and parallel, preconditioned Jacobi–Davidson for large, sparse symmetric matrices

Bergamaschi, Luca; Pini, Giorgio; Sartoretto, Flavio

doi:10.1016/s0021-9991(03)00190-6

Cited by 20 publications

(21 citation statements)

References 39 publications

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“…Indeed, preconditioned CG converges when solving JD correction equations, though they are not positive definite. However, we showed in Reference [15] that CG performance in our problems is not any time superior to BiCGSTAB.…”

Section: Sequential Preconditioned Jdmentioning

confidence: 70%

Parallel eigenanalysis of multiaquifer systems

Bergamaschi¹,

Pini²,

Sartoretto

2005

Int. J. Numer. Meth. Engng

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SUMMARYFinite element discretizations of flow problems involving multiaquifer systems deliver large, sparse, unstructured matrices, whose partial eigenanalysis is important for both solving the flow problem and analysing its main characteristics.We studied and implemented an effective preconditioning of the Jacobi-Davidson algorithm by FSAI-type preconditioners.We developed efficient parallelization strategies in order to solve very large problems, which could not fit into the storage available to a single processor.We report our results about the solution of multiaquifer flow problems on an SP4 machine and a Linux Cluster. We analyse the sequential and parallel efficiency of our algorithm, also compared with standard packages. Questions regarding the parallel solution of finite element eigenproblems are addressed and discussed.

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Section: Sequential Preconditioned Jdmentioning

confidence: 70%

Parallel eigenanalysis of multiaquifer systems

Bergamaschi¹,

Pini²,

Sartoretto

2005

Int. J. Numer. Meth. Engng

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“…Because its basic ingredients are matrix-vector products, vector updates and inner products it can be parallelized easily [1]. Its JDQR variant [8], which is based on the computation of a partial Schur form of the system matrix, uses deflation techniques to compute a number of interior eigenpairs.…”

Section: Jacobi-davidson Methodsmentioning

confidence: 99%

Application of the Jacobi–Davidson method for spectral low-rank preconditioning in computational electromagnetics problems

Mas

Cerdán

Malla

et al. 2014

SeMA

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We consider the numerical solution of linear systems arising from computational electromagnetics applications. For large scale problems the solution is usually obtained iteratively with a Krylov subspace method. It is well known that for ill conditioned problems the convergence of these methods can be very slow or even it may be impossible to obtain a satisfactory solution. To improve the convergence a preconditioner can be used, but in some cases additional strategies are needed. In this work we study the application of spectral lowrank updates (SLRU) to a previously computed sparse approximate inverse preconditioner. The updates are based on the computation of a small subset of the eigenpairs closest to the origin. Thus, the performance of the SLRU technique depends on the method available to compute the eigenpairs of interest. The SLRU method was first used using the IRA's method implemented in ARPACK. In this work we investigate the use of a Jacobi-Davidson method, in particular its JDQR variant . The results of the numerical experiments show that the application of the JDQR method to obtain the spectral low-rank updates can be quite competitive compared with the IRA's method.

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“…Finding the smallest eigenvalues and eigenvectors of a sparse and symmetric matrix is a computational problem which has been studied for decades for problems in physics and chemistry [21,22], and can be solved using distributed algorithms for parallel processing. In particular, if sensors select local cluster-heads, the distributed algorithm can use data-distribution techniques and block-Jacobi preconditioning methods to reduce communication.…”

Section: Computationmentioning

confidence: 99%

“…The dwMDS also has a slower increase in communication requirements than centralized localization algorithms as N increases [16]. Furthermore, since prior information is included directly in (22), there is no need to do post-processing.…”

Section: Computationmentioning

confidence: 99%

Learning Sensor Location from Signal Strength and Connectivity

Patwari

Hero

Costa

2007

Advances in Information Security

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Received signal strength (RSS) or connectivity, i.e., whether or not two devices can communicate, are two relatively inexpensive (in terms of device and energy costs) measurements at the receiver that indicate the distance from the transmitter. Such measurements can either be quickly dismissed as too unreliable for localization, or idealized by ignoring the non-circular nature of a transmitter's coverage area. This chapter finds a middle ground between these two extremes by using measurement-based statistical models to represent the inaccuracies of RSS and connectivity.While a particular RSS or connectivity measurement may be hard to predict, a statistical model for RSS and connectivity can in fact be wellcharacterized. Many numerical examples are used to provide the reader with intuition about the variability of real-world RSS and connectivity measurements.This chapter then gives a description of three sensor localization algorithms which are based on 'manifold learning', a class of non-linear dimension reduction methods. These algorithms include Isomap [1], the distributed weighted multi-dimensional scaling (dwMDS) algorithm [2], and the Laplacian Eigenmap adaptive neighbor (LEAN) algorithm [3]. The performance of these estimators is compared via simulation using the RSS and connectivity measurement models.The results show that while RSS and connectivity measurements are highly variable, these manifold learning-based algorithms demonstrate their robustness by achieving location estimates with low bias and often variance close to the lower bound. Due to their desirability as low cost, low complexity mea- * This work was partially funded by the DARPA Defense Sciences Office under Office of Naval Research contract #N00014-04-C-0437. Distribution Statement A. Approved for public release; distribution is unlimited.

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Computational experience with sequential and parallel, preconditioned Jacobi–Davidson for large, sparse symmetric matrices

Cited by 20 publications

References 39 publications

Parallel eigenanalysis of multiaquifer systems

Parallel eigenanalysis of multiaquifer systems

Application of the Jacobi–Davidson method for spectral low-rank preconditioning in computational electromagnetics problems

Learning Sensor Location from Signal Strength and Connectivity

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