{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T17:02:55Z","timestamp":1770742975156,"version":"3.49.0"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T00:00:00Z","timestamp":1746057600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T00:00:00Z","timestamp":1746057600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Comput. Sci. Technol."],"published-print":{"date-parts":[[2025,5]]},"DOI":"10.1007\/s11390-024-3673-8","type":"journal-article","created":{"date-parts":[[2025,7,10]],"date-time":"2025-07-10T09:40:50Z","timestamp":1752140450000},"page":"855-869","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimization of Generalized Eigensolver for Dense Symmetric Matrices on AMD GPU"],"prefix":"10.1007","volume":"40","author":[{"given":"Chong","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zi-Tong","family":"Su","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Min","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui-Yuan","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wen-Jing","family":"Ma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei-Sheng","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,7,9]]},"reference":[{"key":"3673_CR1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719604","volume-title":"LAPACK Users\u2019 Guide","author":"E Anderson","year":"1999","unstructured":"Anderson E, Bai Z, Bischof C, Blackford L S, Demmel J, Dongarra J, Du Croz J, Greenbaum A, Hammarling S, McKenney A, Sorensen D. LAPACK Users\u2019 Guide (3rd edition). Society for Industrial and Applied Mathematics, 1999.","edition":"3rd edition"},{"key":"3673_CR2","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1109\/FMPC.1992.234898","volume-title":"Proc. the 4th Symposium on the Frontiers of Massively Parallel Computation","author":"J Choi","year":"1992","unstructured":"Choi J, Dongarra J J, Pozo R, Walker D W. ScaLA-PACK: A scalable linear algebra library for distributed memory concurrent computers. In Proc. the 4th Symposium on the Frontiers of Massively Parallel Computation, Oct. 1992, pp.120\u2013127. DOI: https:\/\/doi.org\/10.1109\/FMPC.1992.234898."},{"key":"3673_CR3","doi-asserted-by":"publisher","first-page":"178","DOI":"10.1109\/SC.2016.15","volume-title":"Proc. the 16th International Conference for High Performance Computing, Networking, Storage and Analysis","author":"J Kestyn","year":"2016","unstructured":"Kestyn J, Kalantzis V, Polizzi E, Saad Y. PFEAST: A high performance sparse eigenvalue solver using distributed-memory linear solvers. In Proc. the 16th International Conference for High Performance Computing, Networking, Storage and Analysis, Nov. 2016, pp.178\u2013189. DOI: https:\/\/doi.org\/10.1109\/SC.2016.15."},{"key":"3673_CR4","doi-asserted-by":"publisher","first-page":"1113","DOI":"10.1109\/IPDPSW.2018.00171","volume-title":"Proc. the 2018 IEEE International Parallel and Distributed Processing Symposium Workshops","author":"T Fukaya","year":"2018","unstructured":"Fukaya T, Imamura T, Yamamoto Y. A case study on modeling the performance of dense matrix computation: Tridiagonalization in the EigenExa eigensolver on the K computer. In Proc. the 2018 IEEE International Parallel and Distributed Processing Symposium Workshops, May 2018, pp.1113\u20131122. DOI: https:\/\/doi.org\/10.1109\/IPDPSW.2018.00171."},{"key":"3673_CR5","doi-asserted-by":"publisher","first-page":"478","DOI":"10.1007\/3-540-62095-8_51","volume-title":"Proc. the 3rd International Workshop on Applied Parallel Computing. Industrial Computation and Optimization","author":"K J Maschhoff","year":"1996","unstructured":"Maschhoff K J, Sorensen D C. PARPACK: An efficient portable large scale eigenvalue package for distributed memory parallel architectures. In Proc. the 3rd International Workshop on Applied Parallel Computing. Industrial Computation and Optimization, Aug. 1996, pp.478\u2013486. DOI: https:\/\/doi.org\/10.1007\/3-540-62095-8_51."},{"key":"3673_CR6","doi-asserted-by":"publisher","first-page":"448","DOI":"10.1007\/978-3-642-12165-4_36","volume-title":"Proc. the 2010 International Conference on Computational Science and Its Applications","author":"A Nishida","year":"2010","unstructured":"Nishida A. Experience in developing an open source scalable software infrastructure in Japan. In Proc. the 2010 International Conference on Computational Science and Its Applications, Mar. 2010, pp.448\u2013462. DOI: https:\/\/doi.org\/10.1007\/978-3-642-12165-4_36."},{"key":"3673_CR7","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1145\/2304576.2304625","volume-title":"Proc. the 26th ACM International Conference on Supercomputing","author":"F Song","year":"2012","unstructured":"Song F, Tomov S, Dongarra J. Enabling and scaling matrix computations on heterogeneous multi-core and multi-GPU systems. In Proc. the 26th ACM International Conference on Supercomputing, Jun. 2012, pp.365\u2013376. DOI: https:\/\/doi.org\/10.1145\/2304576.2304625."},{"key":"3673_CR8","series-title":"Technical Report DOE-UTK-ER25987-5","doi-asserted-by":"publisher","DOI":"10.2172\/1126489","volume-title":"Matrix algebra for GPU and multicore architectures (MAGMA) for large Petascale systems","author":"J J Dongarra","year":"2014","unstructured":"Dongarra J J, Tomov S. Matrix algebra for GPU and multicore architectures (MAGMA) for large Petascale systems. Technical Report DOE-UTK-ER25987-5, The University of Tennessee, 2014. https:\/\/www.osti.gov\/biblio\/1126489, Feb. 2025."},{"issue":"21","key":"3673_CR9","doi-asserted-by":"publisher","first-page":"213201","DOI":"10.1088\/0953-8984\/26\/21\/213201","volume":"26","author":"A Marek","year":"2014","unstructured":"Marek A, Blum V, Johanni R, Havu V, Lang B, Auckenthaler T, Heinecke A, Bungartz H J, Lederer H. The EL-PA library: Scalable parallel eigenvalue solutions for electronic structure theory and computational science. Journal of Physics: Condensed Matter, 2014, 26(21): 213201. DOI: https:\/\/doi.org\/10.1088\/0953-8984\/26\/21\/213201.","journal-title":"Journal of Physics: Condensed Matter"},{"key":"3673_CR10","doi-asserted-by":"publisher","first-page":"107808","DOI":"10.1016\/j.cpc.2020.107808","volume":"262","author":"V W Z Yu","year":"2021","unstructured":"Yu V W Z, Moussa J, K\u016fs P, Marek A, Messmer P, Yoon M, Lederer H, Blum V. GPU-acceleration of the ELPA2 distributed eigensolver for dense symmetric and Hermitian eigenproblems. Computer Physics Communications, 2021, 262: 107808. DOI: https:\/\/doi.org\/10.1016\/j.cpc.2020.107808.","journal-title":"Computer Physics Communications"},{"key":"3673_CR11","doi-asserted-by":"publisher","DOI":"10.1145\/3295500.3356223","volume-title":"Proc. the 2019 International Conference for High Performance Computing, Networking, Storage and Analysis","author":"M Gates","year":"2019","unstructured":"Gates M, Kurzak J, Charara A, YarKhan A, Dongarra J. SLATE: Design of a modern distributed and accelerated linear algebra library. In Proc. the 2019 International Conference for High Performance Computing, Networking, Storage and Analysis, Nov. 2019, Article No. 26. DOI: https:\/\/doi.org\/10.1145\/3295500.3356223."},{"issue":"5\/6","key":"3673_CR12","doi-asserted-by":"publisher","first-page":"232 240","DOI":"10.1016\/j.parco.2009.12.005","volume":"36","author":"S Tomov","year":"2010","unstructured":"Tomov S, Dongarra J, Baboulin M. Towards dense linear algebra for hybrid GPU accelerated manycore systems. Parallel Computing, 2010, 36(5\/6): 232 240. DOI: https:\/\/doi.org\/10.1016\/j.parco.2009.12.005.","journal-title":"Parallel Computing"},{"issue":"2","key":"3673_CR13","doi-asserted-by":"publisher","first-page":"C70","DOI":"10.1137\/100806783","volume":"34","author":"C V\u00f6mel","year":"2012","unstructured":"V\u00f6mel C, Tomov S, Dongarra J. Divide and conquer on hybrid GPU-accelerated multicore systems. SIAM Journal on Scientific Computing, 2012, 34(2): C70\u2013C82. DOI: https:\/\/doi.org\/10.1137\/100806783.","journal-title":"SIAM Journal on Scientific Computing"},{"key":"3673_CR14","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719628","volume-title":"ARPACK Users\u2019 Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods","author":"R B Lehoucq","year":"1998","unstructured":"Lehoucq R B, Sorensen D C, Yang C. ARPACK Users\u2019 Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. Society for Industrial and Applied Mathematics, 1998."},{"issue":"1","key":"3673_CR15","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1137\/S0895479892241287","volume":"16","author":"M Gu","year":"1995","unstructured":"Gu M, Eisenstat S C. A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem. SIAM Journal on Matrix Analysis and Applications, 1995, 16(1): 172\u2013191. DOI: https:\/\/doi.org\/10.1137\/S0895479892241287.","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"issue":"2","key":"3673_CR16","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1109\/TC.1977.5009293","volume":"C-26","author":"A H Sameh","year":"1977","unstructured":"Sameh A H, Kuck D J. A parallel QR algorithm for symmetric tridiagonal matrices. IEEE Trans. Computers, 1977, C-26(2): 147\u2013153. DOI: https:\/\/doi.org\/10.1109\/TC.1977.5009293.","journal-title":"IEEE Trans. Computers"},{"issue":"4","key":"3673_CR17","doi-asserted-by":"publisher","first-page":"533 560","DOI":"10.1145\/1186785.1186788","volume":"32","author":"I S Dhillon","year":"2006","unstructured":"Dhillon I S, Parlett B N, V\u00f6mel C. The design and implementation of the MRRR algorithm. ACM Trans. Mathematical Software, 2006, 32(4): 533 560. DOI: https:\/\/doi.org\/10.1145\/1186785.1186788.","journal-title":"ACM Trans. Mathematical Software"},{"issue":"16","key":"3673_CR18","doi-asserted-by":"publisher","first-page":"2652 2666","DOI":"10.1002\/cpe.3152","volume":"26","author":"I Yamazaki","year":"2014","unstructured":"Yamazaki I, Dong T, Solc\u00e0 R, Tomov S, Dongarra J, Schulthess T. Tridiagonalization of a dense symmetric matrix on multiple GPUs and its application to symmetric eigenvalue problems. Concurrency and Computation: Practice and Experience, 2014, 26(16): 2652 2666. DOI: https:\/\/doi.org\/10.1002\/cpe.3152.","journal-title":"Concurrency and Computation: Practice and Experience"},{"issue":"12","key":"3673_CR19","doi-asserted-by":"publisher","first-page":"2635","DOI":"10.7544\/issn1000-1239.2020.20190731","volume":"57","author":"S Liu","year":"2020","unstructured":"Liu S, Zhao Y, Yu T, Huang R. Efficient implementation of parallel symmetric matrix tridiagonalization algorithm on GPU cluster. Journal of Computer Research and Development, 2020, 57(12): 2635\u20132647. DOI: https:\/\/doi.org\/10.7544\/issn1000-1239.2020.20190731. (in Chinese)","journal-title":"Journal of Computer Research and Development"},{"issue":"12","key":"3673_CR20","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1016\/j.parco.2010.06.001","volume":"36","author":"S Tomov","year":"2010","unstructured":"Tomov S, Nath R, Dongarra J. Accelerating the reduction to upper Hessenberg, tridiagonal, and bidiagonal forms through hybrid GPU-based computing. Parallel Computing, 2010, 36(12): 645\u2013654. DOI: https:\/\/doi.org\/10.1016\/j.parco.2010.06.001.","journal-title":"Parallel Computing"},{"key":"3673_CR21","doi-asserted-by":"publisher","DOI":"10.1109\/HPEC43674.2020.9286214","volume-title":"Proc. the 2020 IEEE High Performance Extreme Computing Conference","author":"C Brown","year":"2020","unstructured":"Brown C, Abdelfattah A, Tomov S, Dongarra J. Design, optimization, and benchmarking of dense linear algebra algorithms on AMD GPUs. In Proc. the 2020 IEEE High Performance Extreme Computing Conference, Sept. 2020. DOI: https:\/\/doi.org\/10.1109\/HPEC43674.2020.9286214."},{"key":"3673_CR22","doi-asserted-by":"publisher","first-page":"Nov","DOI":"10.1145\/2063384.2063392","volume-title":"Proc. the 2011 International Conference for High Performance Computing, Networking, Storage and Analysis","author":"R Nath","year":"2011","unstructured":"Nath R, Tomov S, Dong T, Dongarra J. Optimizing symmetric dense matrix-vector multiplication on GPUs. In Proc. the 2011 International Conference for High Performance Computing, Networking, Storage and Analysis, Nov. 2011, Article No. 6. DOI: https:\/\/doi.org\/10.1145\/2063384.2063392."},{"key":"3673_CR23","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1007\/978-3-642-38718-0_10","volume-title":"Proc. the 10th International Conference on High Performance Computing for Computational Science","author":"A Abdelfattah","year":"2012","unstructured":"Abdelfattah A, Dongarra J, Keyes D, Ltaief H. Optimizing memory-bound SYMV kernel on GPU hardware accelerators. In Proc. the 10th International Conference on High Performance Computing for Computational Science, Jul. 2012, pp.72\u201379. DOI: https:\/\/doi.org\/10.1007\/978-3-642-38718-0_10."},{"key":"3673_CR24","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/978-3-642-36949-0_23","volume-title":"Proc. the 18th International Conference on Parallel Processing Workshops","author":"A Abdelfattah","year":"2012","unstructured":"Abdelfattah A, Keyes D, Ltaief H. Systematic approach in optimizing numerical memory-bound kernels on GPU. In Proc. the 18th International Conference on Parallel Processing Workshops, Aug. 2012, pp.207\u2013216. DOI: https:\/\/doi.org\/10.1007\/978-3-642-36949-0_23."},{"key":"3673_CR25","doi-asserted-by":"publisher","unstructured":"Abdelfattah A, Keyes D, Ltaief H. KBLAS: An optimized library for dense matrix-vector multiplication on GPU accelerators. ACM Trans. Mathematical Software, 2016, 42(3): Article No. 18. DOI: https:\/\/doi.org\/10.1145\/2818311.","DOI":"10.1145\/2818311"},{"key":"3673_CR26","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1145\/3559009.3569666","volume-title":"Proc. the 2022 International Conference on Parallel Architectures and Compilation Techniques","author":"Y Bao","year":"2022","unstructured":"Bao Y, Sun Y, Feric Z, Shen M T, Weston M, Abell\u00e1n J L, Baruah T, Kim J, Joshi A, Kaeli D. NaviSim: A highly accurate GPU simulator for AMD RDNA GPUs. In Proc. the 2022 International Conference on Parallel Architectures and Compilation Techniques, Oct. 2022, pp.333\u2013345. DOI: https:\/\/doi.org\/10.1145\/3559009.3569666."},{"key":"3673_CR27","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1109\/IA354616.2021.00010","volume-title":"Proc. the 11th IEEE\/ACM Workshop on Irregular Applications: Architectures and Algorithms","author":"C P Stone","year":"2021","unstructured":"Stone C P, Walden A, Zubair M, Nielsen E J. Accelerating unstructured-grid CFD algorithms on NVIDIA and AMD GPUs. In Proc. the 11th IEEE\/ACM Workshop on Irregular Applications: Architectures and Algorithms, Nov. 2021, pp.19\u201326. DOI: https:\/\/doi.org\/10.1109\/IA354616.2021.00010."},{"issue":"2","key":"3673_CR28","doi-asserted-by":"publisher","first-page":"254","DOI":"10.1137\/S0036144596300773","volume":"39","author":"I C F Ipsen","year":"1997","unstructured":"Ipsen I C F. Computing an eigenvector with inverse iteration. SIAM Review, 1997, 39(2): 254\u2013291. DOI: https:\/\/doi.org\/10.1137\/S0036144596300773.","journal-title":"SIAM Review"},{"key":"3673_CR29","doi-asserted-by":"publisher","DOI":"10.56021\/9781421407944","volume-title":"Matrix Computations","author":"G H Golub","year":"2013","unstructured":"Golub G H, Van Loan C F. Matrix Computations (4th edition). Johns Hopkins University Press, 2013.","edition":"4th edition"},{"key":"3673_CR30","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719642","volume-title":"ScaLAPACK Users\u2019 Guide","author":"L S Blackford","year":"1997","unstructured":"Blackford L S, Choi J, Cleary A, D\u2019Azevedo E, Demmel J, Dhillon I, Dongarra J, Hammarling S, Henry G, Petitet A, Stanley K, Walker D, Whaley R C. ScaLAPACK Users\u2019 Guide. Society for Industrial and Applied Mathematics, 1997."},{"issue":"6","key":"3673_CR31","doi-asserted-by":"publisher","first-page":"3495","DOI":"10.1137\/090760969","volume":"32","author":"G Ballard","year":"2010","unstructured":"Ballard G, Demmel J, Holtz O, Schwartz O. Communication-optimal parallel and sequential Cholesky decomposition. SIAM Journal on Scientific Computing, 2010, 32(6): 3495\u20133523. DOI: https:\/\/doi.org\/10.1137\/090760969.","journal-title":"SIAM Journal on Scientific Computing"}],"container-title":["Journal of Computer Science and Technology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11390-024-3673-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11390-024-3673-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11390-024-3673-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,7]],"date-time":"2025-09-07T02:20:47Z","timestamp":1757211647000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11390-024-3673-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5]]},"references-count":31,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,5]]}},"alternative-id":["3673"],"URL":"https:\/\/doi.org\/10.1007\/s11390-024-3673-8","relation":{},"ISSN":["1000-9000","1860-4749"],"issn-type":[{"value":"1000-9000","type":"print"},{"value":"1860-4749","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,5]]},"assertion":[{"value":"12 August 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 May 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 July 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"Conflict of Interest The authors declare that they have no conflict of interest.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics"}}]}}