{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T09:55:12Z","timestamp":1760522112369,"version":"3.41.0"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"1-4","license":[{"start":{"date-parts":[[2000,9,1]],"date-time":"2000-09-01T00:00:00Z","timestamp":967766400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2000,9,1]],"date-time":"2000-09-01T00:00:00Z","timestamp":967766400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Algorithms"],"published-print":{"date-parts":[[2000,9]]},"DOI":"10.1023\/a:1016656923184","type":"journal-article","created":{"date-parts":[[2002,12,29]],"date-time":"2002-12-29T18:09:18Z","timestamp":1041185358000},"page":"89-107","source":"Crossref","is-referenced-by-count":8,"title":["An L-ribbon for large underdetermined linear discrete ill-posed problems"],"prefix":"10.1007","volume":"25","author":[{"given":"D.","family":"Calvetti","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"Morigi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L.","family":"Reichel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F.","family":"Sgallari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"318422_CR1","doi-asserted-by":"crossref","DOI":"10.1887\/0750304359","volume-title":"Introduction to Inverse Problems in Imaging","author":"M. Bertero","year":"1998","unstructured":"M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Institute of Physics Publ., Bristol, 1998)."},{"key":"318422_CR2","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1023\/A:1022383005969","volume":"39","author":"D. Calvetti","year":"1999","unstructured":"D. Calvetti, G.H. Golub and L. Reichel, Estimation of the L-curve via Lanczos bidiagonalization, BIT 39 (1999) 603\u2013619.","journal-title":"BIT"},{"key":"318422_CR3","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1016\/S0377-0427(00)00414-3","volume":"123","author":"D. Calvetti","year":"2000","unstructured":"D. Calvetti, S. Morigi, L. Reichel and F. Sgallari, Tikhonov regularization and the L-curve for large discrete ill-posed problems, J. Comput. Appl. Math. 123 (2000) 423\u2013446.","journal-title":"J. Comput. Appl. Math."},{"key":"318422_CR4","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/S0377-0427(99)00298-8","volume":"115","author":"D. Calvetti","year":"2000","unstructured":"D. Calvetti, L. Reichel, F. Sgallari and G. Spaletta, A regularizing Lanczos iteration method for underdetermined linear systems, J. Comput. Appl. Math. 115 (2000) 101\u2013120.","journal-title":"J. Comput. Appl. Math."},{"key":"318422_CR5","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1007\/BF01932285","volume":"17","author":"L. Eld\u00e9n","year":"1977","unstructured":"L. Eld\u00e9n, Algorithms for the regularization of ill-conditioned least squares problems, BIT 17 (1977) 134\u2013145.","journal-title":"BIT"},{"key":"318422_CR6","first-page":"105","volume-title":"Numerical Analysis 1993","author":"G.H. Golub","year":"1994","unstructured":"G.H. Golub and G. Meurant, Matrices, moments and quadrature, in: Numerical Analysis 1993, eds. D.F. Griffiths and G.A. Watson (Longman, Essex, 1994) pp. 105\u2013156."},{"key":"318422_CR7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/10618600.1997.10474725","volume":"6","author":"G.H. Golub","year":"1997","unstructured":"G.H. Golub and U. von Matt, Generalized cross-validation for large scale problems, J. Comput. Graph. Stat. 6 (1997) 1\u201334.","journal-title":"J. Comput. Graph. Stat."},{"key":"318422_CR8","doi-asserted-by":"crossref","first-page":"561","DOI":"10.1137\/1034115","volume":"34","author":"P.C. Hansen","year":"1992","unstructured":"P.C. Hansen, Analysis of discrete ill-posed problems by means of the L-curve, SIAM Review 34 (1992) 561\u2013580.","journal-title":"SIAM Review"},{"key":"318422_CR9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02149761","volume":"6","author":"P.C. Hansen","year":"1994","unstructured":"P.C. Hansen, Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems, Numer. Algorithms 6 (1994) 1\u201335.","journal-title":"Numer. Algorithms"},{"key":"318422_CR10","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719697","volume-title":"Rank-Deficient and Discrete Ill-Posed Problems","author":"P.C. Hansen","year":"1998","unstructured":"P.C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems (SIAM, Philadelphia, PA, 1998)."},{"key":"318422_CR11","doi-asserted-by":"crossref","first-page":"1487","DOI":"10.1137\/0914086","volume":"14","author":"P.C. Hansen","year":"1993","unstructured":"P.C. Hansen and D.P. O'Leary, The use of the L-curve in the regularization of discrete ill-posed problems, SIAM J. Sci. Comput. 14 (1993) 1487\u20131503.","journal-title":"SIAM J. Sci. Comput."},{"key":"318422_CR12","volume-title":"Image Reconstruction from Projections","author":"G.T. Herman","year":"1980","unstructured":"G.T. Herman, Image Reconstruction from Projections (Academic Press, New York, 1980)."},{"key":"318422_CR13","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1080\/10618600.1997.10474753","volume":"6","author":"L. Kaufman","year":"1997","unstructured":"L. Kaufman and A. Neumaier, Regularization of ill-posed problems by envelope guided conjugate gradients, J. Comput. Graph. Stat. 6 (1997) 451\u2013463.","journal-title":"J. Comput. Graph. Stat."},{"key":"318422_CR14","unstructured":"S. Morigi and F. Sgallari, A regularizing L-curve Lanczos method for underdetermined linear systems, Appl. Math. Comput., in press."},{"key":"318422_CR15","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1145\/355984.355989","volume":"8","author":"C.C. Paige","year":"1982","unstructured":"C.C. Paige and M.A. Saunders, LSQR: An algorithm for sparse linear equations and sparse least squares, ACM Trans. Math. Software 8 (1982) 43\u201371.","journal-title":"ACM Trans. Math. Software"},{"key":"318422_CR16","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/0022-247X(72)90259-4","volume":"37","author":"C.B. Shaw Jr.","year":"1972","unstructured":"C.B. Shaw, Jr., Improvements of the resolution of an instrument by numerical solution of an integral equation, J. Math. Anal. Appl. 37 (1972) 83\u2013112.","journal-title":"J. Math. Anal. Appl."},{"key":"318422_CR17","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-05156-2","volume-title":"Matrix Iterative Analysis","author":"R.S. Varga","year":"2000","unstructured":"R.S. Varga, Matrix Iterative Analysis, 2nd ed. (Springer, New York, 2000).","edition":"2nd ed."},{"key":"318422_CR18","volume-title":"The Algebraic Eigenvalue Problem","author":"J.H. Wilkinson","year":"1965","unstructured":"J.H. Wilkinson, The Algebraic Eigenvalue Problem (Oxford Univ. Press, Oxford, 1965)."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1016656923184.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1016656923184\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1016656923184.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T07:19:50Z","timestamp":1751872790000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1016656923184"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,9]]},"references-count":18,"journal-issue":{"issue":"1-4","published-print":{"date-parts":[[2000,9]]}},"alternative-id":["318422"],"URL":"https:\/\/doi.org\/10.1023\/a:1016656923184","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2000,9]]}}}