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After the introduction of this refinement technique it is shown that, by combining levels of refinement, a preconditioner of optimal order can be constructed for the case of local refinement along a line. Its relative condition number is accurately estimated. Numerical tests demonstrating the performance of the proposed preconditioners will be reported in a forthcoming paper.<\/jats:p>","DOI":"10.1002\/nla.1680020404","type":"journal-article","created":{"date-parts":[[2005,11,1]],"date-time":"2005-11-01T19:23:17Z","timestamp":1130872997000},"page":"347-361","source":"Crossref","is-referenced-by-count":2,"title":["Optimal algebraic multilevel preconditioning for local refinement along a line"],"prefix":"10.1002","volume":"2","author":[{"given":"S.","family":"Margenov","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Maubach","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2005,7,8]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"J. M.Aarden. Thesis in preparation. 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