Numerical analysis of parallel implementation of the reorthogonalized ABS methods

Fodor, Szabina; Nemeth, Zoltan A

doi:10.1007/s10100-018-0557-4

Cited by 2 publications

(4 citation statements)

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“…One solution to speed up the algorithm may be to parallelize the processes. In a recent paper [30], we found that for a real ABS algorithm, parallelization yielded a significant gain in computational speed.…”

Section: Remarkmentioning

confidence: 98%

“…The H i H i = H i feature of our algorithm enables further potential improvement in computational accuracy of the scaled complex ABS algorithm. We have recently published that the reprojection of real ABS algorithms, i.e., using p i = H H i (H H i z i ) projection vectors instead of p i = H H i z i , enhances the precision of numerical calculation [30,31], which expands the practical usefulness of our algorithms. Theorem 3.…”

Section: Remarkmentioning

confidence: 99%

“…These algorithms can also be used for various other purposes such as solving non-linear systems of equations or optimization problems [26][27][28]. ABS-based algorithms can be easily and effectively parallelised [29,30] which underlines the practical usefulness of these algorithms.…”

Section: Introductionmentioning

confidence: 99%

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ABS-Based Direct Method for Solving Complex Systems of Linear Equations

Abaffy

Fodor

2021

Mathematics

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Efficient solution of linear systems of equations is one of the central topics of numerical computation. Linear systems with complex coefficients arise from various physics and quantum chemistry problems. In this paper, we propose a novel ABS-based algorithm, which is able to solve complex systems of linear equations. Theoretical analysis is given to highlight the basic features of our new algorithm. Four variants of our algorithm were also implemented and intensively tested on randomly generated full and sparse matrices and real-life problems. The results of numerical experiments reveal that our ABS-based algorithm is able to compute the solution with high accuracy. The performance of our algorithm was compared with a commercially available software, Matlab’s mldivide (\) algorithm. Our algorithm outperformed the Matlab algorithm in most cases in terms of computational accuracy. These results expand the practical usefulness of our algorithm.

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Section: Remarkmentioning

confidence: 98%

Section: Remarkmentioning

confidence: 99%

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ABS-Based Direct Method for Solving Complex Systems of Linear Equations

Abaffy

Fodor

2021

Mathematics

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“…The composition of the special issue reflects more or less the versatility of the conference subjects. More than half of our papers investigate methodological issues: those written by Borgulya (2018), Baumgartner et al (2018), Bódis and Balogh (2018), Cafuta (2018), Eisenberg-Nagy et al (2018, Fodor and Németh (2018), Leitold et al (2018), and Molnár-Szipai and Varga (2018). The contribution by Dobos and Vörösmarty (2018), considers an economic problem.…”

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confidence: 99%