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By looking at the local structure of the coefficient matrix and performing a recursive set of variable eliminations, combined with a simplification of the resulting coarse level problems, we obtain bases better suited for problems with inhomogeneous (spatially varying) data, smoothness, and boundary constraints. Our approach removes the need to heuristically adjust the optimal number of preconditioning levels, significantly outperforms previously proposed approaches, and also maps cleanly onto data-parallel architectures such as modern GPUs.<\/jats:p>","DOI":"10.1145\/1141911.1142005","type":"journal-article","created":{"date-parts":[[2006,7,25]],"date-time":"2006-07-25T14:14:26Z","timestamp":1153836866000},"page":"1135-1143","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":80,"title":["Locally adapted hierarchical basis preconditioning"],"prefix":"10.1145","volume":"25","author":[{"given":"Richard","family":"Szeliski","sequence":"first","affiliation":[{"name":"Microsoft Research"}]}],"member":"320","published-online":{"date-parts":[[2006,7]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/1015706.1015718"},{"key":"e_1_2_2_2_1","unstructured":"Bathe K.-J. and Wilson E. L. 1976. 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