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It is proved that the preconditioning procedure minimizes the remaining transportation cost among all admissible affine maps. The procedure can be used on both continuous measures and finite sample sets from distributions. In numerical examples, the procedure is applied to multivariate normal distributions, to a two-dimensional shape transform problem, and to color-transfer problems.<\/jats:p>","DOI":"10.1137\/16m1074953","type":"journal-article","created":{"date-parts":[[2017,8,31]],"date-time":"2017-08-31T14:28:30Z","timestamp":1504189710000},"page":"A1793-A1810","source":"Crossref","is-referenced-by-count":6,"title":["Preconditioning of Optimal Transport"],"prefix":"10.1137","volume":"39","author":[{"given":"Max","family":"Kuang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Esteban G.","family":"Tabak","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,8,31]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2012.120"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/100805741"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050002"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160440402"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/040619831"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/BF02214649"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(1989)046<2684:POTLSE>2.0.CO;2"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.4310\/CDM.1997.v1997.n1.a2"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12671"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/1788425"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1307\/mmj\/1029003026"},{"key":"atypb13","first-page":"1383","volume":"133","author":"Kantorovich L. 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