{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T14:42:03Z","timestamp":1698331323451},"reference-count":27,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2005,7,8]],"date-time":"2005-07-08T00:00:00Z","timestamp":1120780800000},"content-version":"vor","delay-in-days":4086,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[1994,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper presents a row relaxation method for solving the regularized \u2113<jats:italic>p<\/jats:italic> least norm problem <jats:disp-formula>\n\n<\/jats:disp-formula> where e and p are positive constants, 1&lt;<jats:italic>p<\/jats:italic>&lt;\u221e The interest that we have in this problem lies in the observation that for small values of E the minimizer of P (X ) is a good substitute for a minimizer of the unregularized problem <jats:disp-formula>\n\n<\/jats:disp-formula> It is shown that the dual of the regularized problem has the form <jats:disp-formula>\n\n<\/jats:disp-formula> where q = p \/(p \u2010 1). Moreover, if y solves the dual problem then X = A<jats:sup>T<\/jats:sup>y\/\u03f5 solves the primal problem and P(A<jats:sup>T<\/jats:sup>y\/\u03f5) = D(y). Maximizing the dual objective function by changing one variable at a time results in a row relaxation method that resembles Kaczmarz's method. This feature makes the new method suitable for solving large sparse C, problems that arise in computerized tomography, geophysics, and groundwater hydrology. Numerical experiments illustrate the feasibility of our ideas.<\/jats:p>","DOI":"10.1002\/nla.1680010304","type":"journal-article","created":{"date-parts":[[2005,10,14]],"date-time":"2005-10-14T22:49:25Z","timestamp":1129330165000},"page":"247-263","source":"Crossref","is-referenced-by-count":2,"title":["A row relaxation method for large \u2113<sub><i>p<\/i><\/sub> least norm problems"],"prefix":"10.1002","volume":"1","author":[{"given":"Achiya","family":"Dax","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2005,7,8]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1016\/B978-0-12-597050-1.50020-8","volume-title":"Nonlinear Programming","author":"Barrodale I.","year":"1970"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1137\/1023097"},{"key":"e_1_2_1_4_2","volume-title":"An Introduction to Numerical Methods and Optimization Techniques","author":"Daniels R. 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Acad. Plon. Sci. Lett. A"},{"key":"e_1_2_1_20_2","unstructured":"Y.Li.A globally convergent method forLpproblems. Tech. Rep. 91\u20131212 Dept. of Computer Science Cornell University 1991."},{"key":"e_1_2_1_21_2","volume-title":"Solving Lp\u2010norm problems and applications. Tech. Rep. CTC93TR122","author":"Li Y.","year":"1993"},{"key":"e_1_2_1_22_2","volume-title":"Optimization by Vector Space Methods","author":"Luenberger D. G.","year":"1969"},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02253335"},{"key":"e_1_2_1_24_2","volume-title":"Finite Algorithms in Optimization and Data Analysis","author":"Osborne M. 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