Maharani, Maharani and Salhi, Abdellah and Suharto, Rifka Amelia (2018) Enhancing the Stability of Lanczos-type Algorithms by Embedding Interpolation and Extrapolation for the Solution of Systems of Linear Equations. Journal of Mathematical and Fundamental Sciences, 50 (2). pp. 148-165. DOI https://doi.org/10.5614/j.math.fund.sci.2018.50.2.4
Maharani, Maharani and Salhi, Abdellah and Suharto, Rifka Amelia (2018) Enhancing the Stability of Lanczos-type Algorithms by Embedding Interpolation and Extrapolation for the Solution of Systems of Linear Equations. Journal of Mathematical and Fundamental Sciences, 50 (2). pp. 148-165. DOI https://doi.org/10.5614/j.math.fund.sci.2018.50.2.4
Maharani, Maharani and Salhi, Abdellah and Suharto, Rifka Amelia (2018) Enhancing the Stability of Lanczos-type Algorithms by Embedding Interpolation and Extrapolation for the Solution of Systems of Linear Equations. Journal of Mathematical and Fundamental Sciences, 50 (2). pp. 148-165. DOI https://doi.org/10.5614/j.math.fund.sci.2018.50.2.4
Abstract
A new method to treat the inherent instability of Lanczos-type algorithms is introduced. It enables us to capture the properties of the sequence of iterates generated by a Lanczos-type algorithm by interpolating on this sequence of points. The interpolation model found is then used to generate a point that is outside the range. It is expected that this new point will link up the rest of the sequence of points generated by the Lanczos-type algorithm if breakdown does not occur. However, because we assume that the interpolation model captures the properties of the Lanczos sequence, the new point belongs to that sequence since it is generated by the model. This paper introduces the so-called Embedded Interpolation and Extrapolation Model in Lanczos-type Algorithms (EIEMLA). The model was implemented in algorithms A13/B6and A13/B13, which are new variants of the Lanczos algorithm. Individually, these algorithms perform badly on high dimensional systems of linear equations (SLEs). However, with the embedded interpolation and extrapolation models, EIEM A13/B6and EIEM A13/B13, a substantial improvement in the performance on SLEs with up to 105variables can be achieved.
Item Type: | Article |
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Uncontrolled Keywords: | breakdown; extrapolation; EIEM A13/B6; EIEM A13/B13; interpolation; Lanczos-type algorithms; patterns |
Subjects: | Q Science > QA Mathematics |
Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematics, Statistics and Actuarial Science, School of |
SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |
Depositing User: | Unnamed user with email elements@essex.ac.uk |
Date Deposited: | 25 Sep 2018 08:50 |
Last Modified: | 30 Oct 2024 21:12 |
URI: | http://repository.essex.ac.uk/id/eprint/23108 |
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