{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,25]],"date-time":"2026-09-25T05:13:53Z","timestamp":1790313233934,"version":"4.1.0"},"reference-count":51,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/100000086","name":"Directorate for Mathematical and Physical Sciences","doi-asserted-by":"publisher","award":["DMS-1127914"],"award-info":[{"award-number":["DMS-1127914"]}],"id":[{"id":"10.13039\/100000086","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>We develop a generalized hybrid iterative approach for computing solutions to large-scale Bayesian inverse problems. We consider a hybrid algorithm based on the generalized Golub--Kahan bidiagonalization for computing Tikhonov regularized solutions to problems where explicit computation of the square root and inverse of the covariance kernel for the prior covariance matrix is not feasible. This is useful for large-scale problems where covariance kernels are defined on irregular grids or are available only via matrix-vector multiplication, e.g., those from the Mat\u00e9rn class. We show that iterates are equivalent to LSQR iterates applied to a directly regularized Tikhonov problem, after a transformation of variables, and we provide connections to a generalized singular value decomposition filtered solution. Our approach shares many benefits of standard hybrid methods such as avoiding semiconvergence and automatically estimating the regularization parameter. Numerical examples from image processing demonstrate the effectiveness of the described approaches.<\/jats:p>","DOI":"10.1137\/16m1081968","type":"journal-article","created":{"date-parts":[[2017,10,26]],"date-time":"2017-10-26T16:24:40Z","timestamp":1509035080000},"page":"S24-S46","source":"Crossref","is-referenced-by-count":29,"title":["Generalized Hybrid Iterative Methods for Large-Scale Bayesian Inverse Problems"],"prefix":"10.1137","volume":"39","author":[{"given":"Julianne","family":"Chung","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arvind K.","family":"Saibaba","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,10,26]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s10596-013-9364-0"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/120866543"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/30\/7\/075009"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-010-0275-3"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01396012"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2005.10.038"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/21\/4\/014"},{"key":"atypb8","volume-title":"An Introduction to Bayesian Scientific Computing: Ten Lectures on Subjective Computing","volume":"2","author":"Calvetti D.","year":"2007"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1088\/0266-5611\/22\/4\/009"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1137\/080732213"},{"key":"atypb11","first-page":"149","volume":"28","author":"Chung J.","year":"2008","journal-title":"Electron. Trans. Numer. Anal."},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1137\/140975024"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1109\/18.382009"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1002\/ima.20007"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1137\/10079687X"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1137\/130917673"},{"key":"atypb17","first-page":"83","volume":"44","author":"Gazzola S.","year":"2015","journal-title":"Electron. Trans. Numer. Anal."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1137\/1015032"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1979.10489751"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1137\/0702016"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1145\/355945.355946"},{"key":"atypb22","first-page":"253","volume":"3","author":"Hanke M.","year":"1993","journal-title":"Surv. Math. Industry"},{"key":"atypb23","doi-asserted-by":"publisher","DOI":"10.1007\/BF02149761"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718836"},{"key":"atypb25","volume-title":"O'leary","author":"Hansen P. C.","year":"2006"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-009-0239-7"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1216\/JIE-2010-22-3-465"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-015-9990-x"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139020411"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-006-0109-5"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1137\/050645592"},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479899345960"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9868.2011.00777.x"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719512"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780198528418.001.0001"},{"key":"atypb36","doi-asserted-by":"publisher","DOI":"10.1023\/A:1022365112368"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1137\/0902037"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1145\/355993.356000"},{"key":"atypb39","doi-asserted-by":"publisher","DOI":"10.1145\/355984.355989"},{"key":"atypb40","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2003.1203207"},{"key":"atypb41","volume-title":"Gaussian Processes for Machine Learning","author":"Rasmussen C. E.","year":"2006"},{"key":"atypb42","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2010.10.002"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2009.05.026"},{"key":"atypb44","volume-title":"Hybrid and Iteratively Reweighted Regularization by Unbiased Predictive Risk and Weighted GCV, preprint, arXiv:1509.00096","author":"Renaut R. A.","year":"2015"},{"key":"atypb45","doi-asserted-by":"publisher","DOI":"10.1137\/0717059"},{"key":"atypb46","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718003"},{"key":"atypb47","doi-asserted-by":"publisher","DOI":"10.1029\/2011WR011778"},{"key":"atypb48","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(76)90044-6"},{"key":"atypb49","doi-asserted-by":"publisher","DOI":"10.1137\/0713009"},{"key":"atypb50","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898717570"},{"key":"atypb51","volume-title":"Numer. Math. Sci. Comput. 87","author":"Wilkinson J. H.","year":"1965"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/16M1081968","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:08:38Z","timestamp":1787328518000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/16M1081968"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":51,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/16M1081968"],"URL":"https:\/\/doi.org\/10.1137\/16m1081968","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}