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The case of real symmetric positive definite matrices is considered in particular, and several numerical examples are given. This approach has some close relations with Riley's method and with Tikhonov regularization. Moreover, we identify approximately the aforementioned procedure with a true action of preconditioning.<\/jats:p>","DOI":"10.1002\/nla.2335","type":"journal-article","created":{"date-parts":[[2020,9,28]],"date-time":"2020-09-28T12:16:21Z","timestamp":1601295381000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the numerical solution of ill\u2010conditioned linear systems by regularization and iteration"],"prefix":"10.1002","volume":"28","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-4561-4845","authenticated-orcid":false,"given":"Renato","family":"Spigler","sequence":"first","affiliation":[{"name":"Department of Mathematics and Physics Roma Tre University Roma Italy"}]}],"member":"311","published-online":{"date-parts":[[2020,9,28]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2002.7176"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144597321909"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492904000212"},{"issue":"3","key":"e_1_2_8_5_1","first-page":"757","article-title":"Iterative solution of symmetric quasi\u2010definite linear systems [book review]","volume":"60","author":"Benzi M","year":"2018","journal-title":"SIAM Rev"},{"key":"e_1_2_8_6_1","doi-asserted-by":"crossref","first-page":"96","DOI":"10.2307\/2002065","article-title":"Solving systems of linear equations with a positive definite, symmetric, but possibly ill\u2010conditioned matrix","volume":"9","author":"Riley JD","year":"1955","journal-title":"Math Tables Aids Comput"},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971262"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-28483-5"},{"key":"e_1_2_8_9_1","volume-title":"Matrix iterative analysis","author":"Varga RS","year":"1962"},{"key":"e_1_2_8_10_1","volume-title":"Iterative methods for solving partial difference Q3 equations of elliptic type [PhD thesis]","author":"Young DM","year":"1950"},{"key":"e_1_2_8_11_1","volume-title":"Unabridged republication of the 1971 edition","author":"Young DM","year":"2003"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/0010-4655(89)90145-8"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00403-9"},{"key":"e_1_2_8_14_1","first-page":"1035","article-title":"Solution of incorrectly formulated problems and the regularization method","volume":"4","author":"Tikhonov AN","year":"1963","journal-title":"Soviet Math Dokl"},{"issue":"5","key":"e_1_2_8_15_1","first-page":"255","article-title":"Eigenvalues of sums of Hermitian matrices (after A. 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