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Lett. 126 (2022) and MCMA 29:4 (2023)),\nwhere we developed a vector randomized algorithms with iterative refinement for large system of linear algebraic equations.\nWe focus in this paper on the application of the vector randomized iterative refinement algorithm\nto boundary integral equations that solve interior Dirichlet and exterior Neumann boundary value problems for\n2D Laplace equation.<\/jats:p>","DOI":"10.1515\/mcma-2024-2022","type":"journal-article","created":{"date-parts":[[2024,11,14]],"date-time":"2024-11-14T12:51:31Z","timestamp":1731588691000},"page":"375-388","source":"Crossref","is-referenced-by-count":6,"title":["Randomized vector algorithm with iterative refinement for solving boundary integral equations"],"prefix":"10.1515","volume":"30","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3698-7540","authenticated-orcid":false,"given":"Karl K.","family":"Sabelfeld","sequence":"first","affiliation":[{"name":"Institute of Computational Mathematics and Mathematical Geophysics , Russian Academy of Sciences , Novosibirsk , Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Georgy","family":"Agarkov","sequence":"additional","affiliation":[{"name":"Institute of Computational Mathematics and Mathematical Geophysics , Russian Academy of Sciences , Novosibirsk , Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2024,11,14]]},"reference":[{"key":"2024112801151898808_j_mcma-2024-2022_ref_001","doi-asserted-by":"crossref","unstructured":"M.  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Sabelfeld,\nVector algorithms of the Monte Carlo method for solving systems of second-order elliptic equations and the Lam\u00e9 equation,\nDokl. Akad. Nauk SSSR 262 (1982), no. 5, 1076\u20131080."},{"key":"2024112801151898808_j_mcma-2024-2022_ref_008","doi-asserted-by":"crossref","unstructured":"K. K.  Sabelfeld,\nVector Monte Carlo stochastic matrix-based algorithms for large linear systems,\nMonte Carlo Methods Appl. 22 (2016), no. 3, 259\u2013264.","DOI":"10.1515\/mcma-2016-0112"},{"key":"2024112801151898808_j_mcma-2024-2022_ref_009","doi-asserted-by":"crossref","unstructured":"K. K.  Sabelfeld,\nA new randomized vector algorithm for iterative solution of large linear systems,\nAppl. Math. Lett. 126 (2022), Article ID 107830.","DOI":"10.1016\/j.aml.2021.107830"},{"key":"2024112801151898808_j_mcma-2024-2022_ref_010","doi-asserted-by":"crossref","unstructured":"K. K.  Sabelfeld, S.  Kireev and A. E.  Kireeva,\nParallel implementations of randomized vector algorithm for solving large systems of linear equations,\nJ. Supercomputing 79 (2023), 10555\u201310569.","DOI":"10.1007\/s11227-023-05079-5"},{"key":"2024112801151898808_j_mcma-2024-2022_ref_011","doi-asserted-by":"crossref","unstructured":"K. K.  Sabelfeld and A. E.  Kireeva,\nRandomized iterative linear solvers with refinement for large dense matrices,\nMonte Carlo Methods Appl. 29 (2023), no. 4, 357\u2013378.","DOI":"10.1515\/mcma-2023-2013"},{"key":"2024112801151898808_j_mcma-2024-2022_ref_012","doi-asserted-by":"crossref","unstructured":"K. K.  Sabelfeld and N. A.  Simonov,\nRandom Walks on Boundary for Solving PDEs,\nVSP, Utrecht, 1994.","DOI":"10.1515\/9783110942026"},{"key":"2024112801151898808_j_mcma-2024-2022_ref_013","doi-asserted-by":"crossref","unstructured":"K. K.  Sabelfeld and N. A.  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