{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T09:14:58Z","timestamp":1776849298218,"version":"3.51.2"},"reference-count":22,"publisher":"Walter de Gruyter GmbH","issue":"2","funder":[{"DOI":"10.13039\/100000181","name":"Air Force Office of Scientific Research","doi-asserted-by":"publisher","award":["FA9451-18-2-0031"],"award-info":[{"award-number":["FA9451-18-2-0031"]}],"id":[{"id":"10.13039\/100000181","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004488","name":"Hrvatska Zaklada za Znanost","doi-asserted-by":"publisher","award":["HRZZ-9345"],"award-info":[{"award-number":["HRZZ-9345"]}],"id":[{"id":"10.13039\/501100004488","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1522471"],"award-info":[{"award-number":["DMS-1522471"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1624776"],"award-info":[{"award-number":["DMS-1624776"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A filtered subspace iteration for computing a cluster of eigenvalues\nand its accompanying eigenspace, known as \u201cFEAST\u201d, has gained considerable attention in recent years.\nThis work studies issues that arise when FEAST is applied to compute part of the spectrum of an unbounded partial differential operator.\nSpecifically, when the resolvent of the partial differential operator is approximated by the discontinuous Petrov\u2013Galerkin (DPG) method, it is shown that there is no spectral pollution.\nThe theory also provides bounds on the discretization errors in the spectral approximations.\nNumerical experiments for simple operators illustrate the theory and also indicate the value of the algorithm beyond the confines of the theoretical assumptions.\nThe utility of the algorithm is illustrated by applying it to compute guided transverse core modes of a realistic optical fiber.<\/jats:p>","DOI":"10.1515\/cmam-2019-0030","type":"journal-article","created":{"date-parts":[[2019,3,27]],"date-time":"2019-03-27T20:18:27Z","timestamp":1553717907000},"page":"251-266","source":"Crossref","is-referenced-by-count":9,"title":["Analysis of FEAST Spectral Approximations Using the DPG Discretization"],"prefix":"10.1515","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7508-3232","authenticated-orcid":false,"given":"Jay","family":"Gopalakrishnan","sequence":"first","affiliation":[{"name":"Portland State University , PO Box 751 , Portland , OR 97207-0751 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3370-9353","authenticated-orcid":false,"given":"Luka","family":"Grubi\u0161i\u0107","sequence":"additional","affiliation":[{"name":"University of Zagreb , Bijenicka 30, 10000 Zagreb , Croatia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1944-2872","authenticated-orcid":false,"given":"Jeffrey","family":"Ovall","sequence":"additional","affiliation":[{"name":"Portland State University , PO Box 751 , Portland , OR 97207-0751 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7671-8607","authenticated-orcid":false,"given":"Benjamin","family":"Parker","sequence":"additional","affiliation":[{"name":"Portland State University , PO Box 751 , Portland , OR 97207-0751 , USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2019,3,27]]},"reference":[{"key":"2023033110021951323_j_cmam-2019-0030_ref_001_w2aab3b7e3831b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"W.-J.  Beyn,\nAn integral method for solving nonlinear eigenvalue problems,\nLinear Algebra Appl. 436 (2012), no. 10, 3839\u20133863.","DOI":"10.1016\/j.laa.2011.03.030"},{"key":"2023033110021951323_j_cmam-2019-0030_ref_002_w2aab3b7e3831b1b6b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"T.  Bouma, J.  Gopalakrishnan and A.  Harb,\nConvergence rates of the DPG method with reduced test space degree,\nComput. Math. Appl. 68 (2014), no. 11, 1550\u20131561.","DOI":"10.1016\/j.camwa.2014.08.004"},{"key":"2023033110021951323_j_cmam-2019-0030_ref_003_w2aab3b7e3831b1b6b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"T.  B\u00fchler and D. A.  Salamon,\nFunctional Analysis,\nGrad. Stud. Math. 191,\nAmerican Mathematical Society, Providence, 2018.","DOI":"10.1090\/gsm\/191"},{"key":"2023033110021951323_j_cmam-2019-0030_ref_004_w2aab3b7e3831b1b6b1ab2ab4Aa","doi-asserted-by":"crossref","unstructured":"C.  Carstensen, L.  Demkowicz and J.  Gopalakrishnan,\nA posteriori error control for DPG methods,\nSIAM J. Numer. Anal. 52 (2014), no. 3, 1335\u20131353.","DOI":"10.1137\/130924913"},{"key":"2023033110021951323_j_cmam-2019-0030_ref_005_w2aab3b7e3831b1b6b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"C.  Carstensen, L.  Demkowicz and J.  Gopalakrishnan,\nBreaking spaces and forms for the DPG method and applications including Maxwell equations,\nComput. Math. Appl. 72 (2016), no. 3, 494\u2013522.","DOI":"10.1016\/j.camwa.2016.05.004"},{"key":"2023033110021951323_j_cmam-2019-0030_ref_006_w2aab3b7e3831b1b6b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"C.  Carstensen and F.  Hellwig,\nOptimal convergence rates for adaptive lowest-order discontinuous Petrov\u2013Galerkin schemes,\nSIAM J. Numer. Anal. 56 (2018), no. 2, 1091\u20131111.","DOI":"10.1137\/17M1146671"},{"key":"2023033110021951323_j_cmam-2019-0030_ref_007_w2aab3b7e3831b1b6b1ab2ab7Aa","doi-asserted-by":"crossref","unstructured":"L.  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