Matching high performance approximate inverse preconditioning to architectural platforms

Giannoutakis, Konstantinos M.; Gravvanis, George A.; Clayton, Brian C.; Patil, Archana; Enright, T.; Morrison, John P.

doi:10.1007/s11227-007-0129-1

Cited by 6 publications

(11 citation statements)

References 13 publications

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“…[20,23,27,37,40,42,43,46,49]. Numerical results have been presented on a number of papers by the author, cf.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…For small values of the "retention" parameter δl, the ratio is large enough to maintain speedups to low values, while increasing δl the ratio tends to zero yielding high speedups, cf. [27].…”

Section: Parallel Conjugate Gradient Methods For Multicomputer Systemsmentioning

confidence: 99%

“…More specifically, for all clusters it has been observed that the optimum tuples (δl, no_proc) for a specific n are of the following order, cf. [27]:…”

Section: Parallel Conjugate Gradient Methods For Multicomputer Systemsmentioning

confidence: 99%

“…[27,65]. Similarly, the Parallel Normalized Explicit Preconditioned Conjugate Gradient-Chronopoulos Gear variant (PNEPCGChG-variant) method, for solving linear systems on distributed memory systems, cf.…”

Section: Parallel Conjugate Gradient Methods For Multicomputer Systemsmentioning

confidence: 99%

“…[1,14,16,24,27,37,40,42,65]. The convergence analysis of normalized approximate inverse preconditioning has been presented in [29,38].…”

Section: Parallel Conjugate Gradient Methods For Multicomputer Systemsmentioning

confidence: 99%

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High Performance Inverse Preconditioning

Gravvanis

2008

Arch Computat Methods Eng

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The derivation of parallel numerical algorithms for solving sparse linear systems on modern computer systems and software platforms has attracted the attention of many researchers over the years. In this paper we present an overview on the design issues of parallel approximate inverse matrix algorithms, based on an antidiagonal "wave pattern" approach and a "fish-bone" computational procedure, for computing explicitly various families of exact and approximate inverses for solving sparse linear systems. Parallel preconditioned conjugate gradienttype schemes in conjunction with parallel approximate inverses are presented for the efficient solution of sparse linear systems. Applications of the proposed parallel methods by solving characteristic sparse linear systems on symmetric multiprocessor systems and distributed systems are discussed and the parallel performance of the proposed schemes is given, using MPI, OpenMP and Java multithreading.

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“…[20,23,27,37,40,42,43,46,49]. Numerical results have been presented on a number of papers by the author, cf.…”

Section: Numerical Resultsmentioning

confidence: 99%

Section: Parallel Conjugate Gradient Methods For Multicomputer Systemsmentioning

confidence: 99%

“…More specifically, for all clusters it has been observed that the optimum tuples (δl, no_proc) for a specific n are of the following order, cf. [27]:…”

Section: Parallel Conjugate Gradient Methods For Multicomputer Systemsmentioning

confidence: 99%

Section: Parallel Conjugate Gradient Methods For Multicomputer Systemsmentioning

confidence: 99%

“…[1,14,16,24,27,37,40,42,65]. The convergence analysis of normalized approximate inverse preconditioning has been presented in [29,38].…”

Section: Parallel Conjugate Gradient Methods For Multicomputer Systemsmentioning

confidence: 99%

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High Performance Inverse Preconditioning

Gravvanis

2008

Arch Computat Methods Eng

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Software rejuvenation and resource reservation policies for optimizing server resource availability using cyclic nonhomogeneous Markov chains

Koutras

Platis

Gravvanis

2012

Appl Stoch Models Bus & Ind

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Software rejuvenation is modeled in a client–server system, which provides resources to priority classes of users. To assure availability, resource reservation policies are adopted for the higher priority classes. In addition software rejuvenation is proposed to optimize resource availability. The system is modeled by a cyclic nonhomogeneous Markov chain to capture the variation of the arrival and service rates during a day period. An optimization problem is solved based on a similar previous work and given the optimal resource reservation policy obtained by its solution, rejuvenation is performed and the optimal rejuvenation policy is determined. As a measure of resource availability the blocking probability of each priority class is used. Performability indicators expressing the total cost are also derived, with respect to the optimal resource reservation and optimal rejuvenation policies, to examine whether rejuvenation benefits the system in terms of cost. To derive the blocking probabilities, the limiting probability distribution is computed using explicit generalized approximate inverse preconditioning for solving efficiently sparse linear systems of algebraic equations. Copyright © 2012 John Wiley & Sons, Ltd.

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