{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T20:44:52Z","timestamp":1771965892473,"version":"3.50.1"},"reference-count":51,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,27]],"date-time":"2022-09-27T00:00:00Z","timestamp":1664236800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["075-15-2022-1121"],"award-info":[{"award-number":["075-15-2022-1121"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this work, we consider the problem of calculating the generalized Moore\u2013Penrose inverse, which is essential in many applications of graph theory. We propose an algorithm for the massively parallel systems based on the recursive algorithm for the generalized Moore\u2013Penrose inverse, the generalized Cholesky factorization, and Strassen\u2019s matrix inversion algorithm. Computational experiments with our new algorithm based on a parallel computing architecture known as the Compute Unified Device Architecture (CUDA) on a graphic processing unit (GPU) show the significant advantages of using GPU for large matrices (with millions of elements) in comparison with the CPU implementation from the OpenCV library (Intel, Santa Clara, CA, USA).<\/jats:p>","DOI":"10.3390\/a15100348","type":"journal-article","created":{"date-parts":[[2022,9,27]],"date-time":"2022-09-27T21:23:27Z","timestamp":1664313807000},"page":"348","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Calculating the Moore\u2013Penrose Generalized Inverse on Massively Parallel Systems"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5439-1057","authenticated-orcid":false,"given":"Vuka\u0161in","family":"Stanojevi\u0107","sequence":"first","affiliation":[{"name":"Faculty of Sciences and Mathematics, University of Ni\u0161, 18000 Ni\u0161, Serbia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0667-4001","authenticated-orcid":false,"given":"Lev","family":"Kazakovtsev","sequence":"additional","affiliation":[{"name":"Laboratory \u201cHybrid Methods of Modelling and Optimization in Complex Systems\u201d, Siberian Federal University, Krasnoyarsk 660041, Russia"},{"name":"Institute of Informatics and Telecomunications, Reshetnev Siberian State University of Science and Technology, Krasnoyarsk 660014, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0655-3741","authenticated-orcid":false,"given":"Predrag S.","family":"Stanimirovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Sciences and Mathematics, University of Ni\u0161, 18000 Ni\u0161, Serbia"},{"name":"Laboratory \u201cHybrid Methods of Modelling and Optimization in Complex Systems\u201d, Siberian Federal University, Krasnoyarsk 660041, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1149-3299","authenticated-orcid":false,"given":"Natalya","family":"Rezova","sequence":"additional","affiliation":[{"name":"Institute of Informatics and Telecomunications, Reshetnev Siberian State University of Science and Technology, Krasnoyarsk 660014, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8257-7329","authenticated-orcid":false,"given":"Guzel","family":"Shkaberina","sequence":"additional","affiliation":[{"name":"Laboratory \u201cHybrid Methods of Modelling and Optimization in Complex Systems\u201d, Siberian Federal University, Krasnoyarsk 660041, Russia"},{"name":"Institute of Informatics and Telecomunications, Reshetnev Siberian State University of Science and Technology, Krasnoyarsk 660014, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wang, G., Wei, Y., and Qiao, S. 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