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## Solving large scale systems of linear equations with a stabilized Lanczos-type algorithms running on a cloud computing platform

#### M. Maharani [1] , A. Salhi [2] , W.K. Mashwani [3] , Ozgur Yeniay [4] , N. Larasati [5] , Triyani Triyani [6]

The Lanczos-type algorithms for Systems of Linear Equations (SLEs) are efficient but fragile. A number of ways to resolve this issue have been suggested. But, the problem is still not fully sorted, in our view. Here, we suggest a way that takes advantage of the sequence of approximate solutions that have been computed prior to breakdown by embedding interpolation/extrapolation to avoid it.  The approach, referred to as Embedded Interpolation-Extrapolation Model in Lanczos-type Algorithm (EIEMLA), generates new iterates which are at least as good as the best in the current sequence. This process is repeated after appending the new iterates to the sequence of approximate solutions until some convergence tolerance is achieved. To improve EIEMLA's convergence and stability, a restart version of REIEMLA is also considered. These algorithms are more robust than other Lanczos-type algorithms, including those with restarting and switching strategies. Both algorithms have been implemented to run in parallel on a Cloud computing platform. Our tests involve SLEs with up to $10^6$ variables and equations. The results show that breakdown is mitigated and efficiency gains can be achieved through parallelization.
Lanczos-type algorithm, breakdown, EIEMLA method, parallel processing, cloud computing
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Birincil Dil en İstatistik ve Olasılık İstatistik Yazar: M. Maharani Yazar: A. Salhi Yazar: W.K. Mashwani (Sorumlu Yazar) Yazar: Ozgur Yeniay Yazar: N. Larasati Yazar: Triyani Triyani Yayımlanma Tarihi : 12 Aralık 2018
 Bibtex @araştırma makalesi { hujms495663, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe Üniversitesi}, year = {2018}, volume = {47}, pages = {1730 - 1741}, doi = {}, title = {Solving large scale systems of linear equations with a stabilized Lanczos-type algorithms running on a cloud computing platform}, key = {cite}, author = {Maharani, M. and Salhi, A. and Mashwani, W.K. and Yeniay, Ozgur and Larasati, N. and Triyani, Triyani} } APA Maharani, M , Salhi, A , Mashwani, W , Yeniay, O , Larasati, N , Triyani, T . (2018). Solving large scale systems of linear equations with a stabilized Lanczos-type algorithms running on a cloud computing platform. Hacettepe Journal of Mathematics and Statistics , 47 (6) , 1730-1741 . Retrieved from https://dergipark.org.tr/tr/pub/hujms/issue/41011/495663 MLA Maharani, M , Salhi, A , Mashwani, W , Yeniay, O , Larasati, N , Triyani, T . "Solving large scale systems of linear equations with a stabilized Lanczos-type algorithms running on a cloud computing platform". Hacettepe Journal of Mathematics and Statistics 47 (2018 ): 1730-1741 Chicago Maharani, M , Salhi, A , Mashwani, W , Yeniay, O , Larasati, N , Triyani, T . "Solving large scale systems of linear equations with a stabilized Lanczos-type algorithms running on a cloud computing platform". Hacettepe Journal of Mathematics and Statistics 47 (2018 ): 1730-1741 RIS TY - JOUR T1 - Solving large scale systems of linear equations with a stabilized Lanczos-type algorithms running on a cloud computing platform AU - M. Maharani , A. Salhi , W.K. Mashwani , Ozgur Yeniay , N. Larasati , Triyani Triyani Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 1730 EP - 1741 VL - 47 IS - 6 SN - 2651-477X-2651-477X M3 - UR - Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Solving large scale systems of linear equations with a stabilized Lanczos-type algorithms running on a cloud computing platform %A M. Maharani , A. Salhi , W.K. Mashwani , Ozgur Yeniay , N. Larasati , Triyani Triyani %T Solving large scale systems of linear equations with a stabilized Lanczos-type algorithms running on a cloud computing platform %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 47 %N 6 %R %U ISNAD Maharani, M. , Salhi, A. , Mashwani, W.K. , Yeniay, Ozgur , Larasati, N. , Triyani, Triyani . "Solving large scale systems of linear equations with a stabilized Lanczos-type algorithms running on a cloud computing platform". Hacettepe Journal of Mathematics and Statistics 47 / 6 (Aralık 2018): 1730-1741 . AMA Maharani M , Salhi A , Mashwani W , Yeniay O , Larasati N , Triyani T . Solving large scale systems of linear equations with a stabilized Lanczos-type algorithms running on a cloud computing platform. Hacettepe Journal of Mathematics and Statistics. 2018; 47(6): 1730-1741. Vancouver Maharani M , Salhi A , Mashwani W , Yeniay O , Larasati N , Triyani T . Solving large scale systems of linear equations with a stabilized Lanczos-type algorithms running on a cloud computing platform. Hacettepe Journal of Mathematics and Statistics. 2018; 47(6): 1741-1730.