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To avoid this problem, a seed\u2010switching technique has been proposed to help switch the seed system to another linear system as a new seed system without losing the dimension of the constructed Krylov subspace. Nevertheless, this technique requires collinear residual vectors when applying Krylov subspace methods to the seed and shifted systems. Since the product\u2010type shifted Krylov subspace methods cannot provide such collinearity, these methods cannot use this technique. In this article, we propose a variant of the shifted BiCGstab method, which possesses the collinearity of residuals, and apply the seed\u2010switching technique to it. Some numerical experiments show that the problem of choosing the initial seed system is circumvented.<\/jats:p>","DOI":"10.1002\/nla.2538","type":"journal-article","created":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T04:03:32Z","timestamp":1698725012000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Shifted LOPBiCG: A locally orthogonal product\u2010type method for solving nonsymmetric shifted linear systems based on Bi\u2010CGSTAB"],"prefix":"10.1002","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9145-8794","authenticated-orcid":false,"given":"Ren\u2010Jie","family":"Zhao","sequence":"first","affiliation":[{"name":"Department of Applied Physics, Graduate School of Engineering Nagoya University  Nagoya Japan"}]},{"given":"Tomohiro","family":"Sogabe","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Graduate School of Engineering Nagoya University  Nagoya Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4060-6288","authenticated-orcid":false,"given":"Tomoya","family":"Kemmochi","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Graduate School of Engineering Nagoya University  Nagoya Japan"}]},{"given":"Shao\u2010Liang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Applied Physics, Graduate School of Engineering Nagoya University  Nagoya Japan"}]}],"member":"311","published-online":{"date-parts":[[2023,10,30]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.73.165108"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-58333-9"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/130914905"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717778"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2019.112396"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2401"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1137\/140979927"},{"key":"e_1_2_9_9_1","unstructured":"BennerP PalittaD SaakJ.Krylov techniques for low\u2010rank ADI. arXiv: 220317174.2022."},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/120902690"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1137\/110834585"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1137\/0712047"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02564277"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1137\/0707032"},{"issue":"49","key":"e_1_2_9_15_1","first-page":"409","article-title":"Methods of conjugate gradients for solving linear systems","volume":"1952","author":"Hestenes MR","year":"1953","journal-title":"J Research Nat Bur Standards."},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1137\/0907058"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1137\/0720023"},{"key":"e_1_2_9_18_1","doi-asserted-by":"publisher","DOI":"10.1137\/0728088"},{"key":"e_1_2_9_19_1","unstructured":"ChronopoulosAT MaS.On squaring Krylov subspace iterative methods for nonsymmetric linear systems. 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