{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:34:55Z","timestamp":1787330095535,"version":"build-2736575974"},"reference-count":32,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"name":"Spanish Ministry of Economy and Competitiveness","award":["SEV-2015-0554"],"award-info":[{"award-number":["SEV-2015-0554"]}]},{"DOI":"10.13039\/100006132","name":"Office of Science","doi-asserted-by":"publisher","award":["DE-AC02-06CH11357"],"award-info":[{"award-number":["DE-AC02-06CH11357"]}],"id":[{"id":"10.13039\/100006132","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006132","name":"Office of Science","doi-asserted-by":"publisher","award":["DE-SC0008877"],"award-info":[{"award-number":["DE-SC0008877"]}],"id":[{"id":"10.13039\/100006132","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1719578"],"award-info":[{"award-number":["DMS-1719578"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>Generalized matrix functions (GMFs) extend the concept of a matrix function to rectangular matrices via the singular value decomposition. Several applications involving directed graphs, Hamiltonian dynamical systems, and optimization problems with low-rank constraints require the action of a GMF of a large, sparse matrix on a vector. We present a new method for applying GMFs to vectors based on Chebyshev interpolation. The method is matrix free and requires no orthogonalization and minimal additional storage. Comparisons against existing approaches based on Lanczos bidiagonalization demonstrate the competitiveness of our approach. We prove that our method is backward stable by generalizing the proof of the backward stability of Clenshaw's algorithm to the matrix case.<\/jats:p>","DOI":"10.1137\/18m1191786","type":"journal-article","created":{"date-parts":[[2019,2,12]],"date-time":"2019-02-12T12:48:27Z","timestamp":1549975707000},"page":"210-234","source":"Crossref","is-referenced-by-count":10,"title":["Stable Computation of Generalized Matrix Functions via Polynomial Interpolation"],"prefix":"10.1137","volume":"40","author":[{"given":"Jared L.","family":"Aurentz","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anthony P.","family":"Austin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michele","family":"Benzi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vassilis","family":"Kalantzis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,2,12]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1090\/proc\/12843"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2014.2358961"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1137\/15M1034131"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1137\/15M1049634"},{"key":"atypb5","unstructured":"J. L. Aurentz,\n                      GPU Accelerated Polynomial Spectral Transformation Methods\n                      , Ph.D. thesis, Washington State University, 2014,https:\/\/doi.org\/2376\/5177."},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2017.06.016"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-006-9057-z"},{"key":"atypb8","doi-asserted-by":"crossref","unstructured":"M. Benzi, D. A. Bini, D. Kressner, H. Munthe-Kaas, and C. Van Loan,\n                      Exploiting Hidden Structure in Matrix Computations: Algorithms and Applications\n                      , Lecture Notes in Math. 2173, Springer, New York, 2016.","DOI":"10.1007\/978-3-319-49887-4"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2012.10.022"},{"key":"atypb10","doi-asserted-by":"crossref","unstructured":"G. Berkolaiko and P. Kuchment,\n                      Introduction to Quantum Graphs\n                      , AMS, Providence, RI, 2013.","DOI":"10.1090\/surv\/186"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1955-0071856-0"},{"key":"atypb12","first-page":"337","volume":"37","author":"Crofts J. J.","year":"2010","journal-title":"Electron. Trans. Numer. Anal."},{"key":"atypb13","first-page":"1","volume":"38","author":"Davis T. A.","year":"2011","journal-title":"ACM Trans. Math. Soft."},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1137\/030600758"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2008.03.011"},{"key":"atypb16","unstructured":"T. A. Driscoll, N. Hale, and L. N. Trefethen, eds.\n                      Chebfun Guide\n                      , Pafnuty Publications, Oxford, 2014."},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/S0041-5553(89)80020-5"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1137\/110836535"},{"key":"atypb19","unstructured":"F. R. Gantmacher,\n                      The Theory of Matrices. Vol.\n                      1, AMS Chelsea Publishing, Providence, RI, 2000."},{"key":"atypb20","unstructured":"G. H. Golub and C. F. Van Loan,\n                      Matrix Computations\n                      , 4th ed., Johns Hopkins University Press, Baltimore, MD, 2013."},{"key":"atypb21","unstructured":"M. Hanke, J. Nagy, and R. Plemmons,\n                      Preconditioned iterative regularization for ill-posed problems\n                      , in Numerical Linear Algebra: Proceedings of the Conference in Numerical Linear Algebra and Scientific Computation (Kent, OH, 1992), L. Reichel, A. Ruttan, and R. S. Varga, eds., de Gruyter, Berlin, 1993, pp. 141-163."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1080\/03081087308817015"},{"key":"atypb23","doi-asserted-by":"crossref","unstructured":"N. J. Higham,\n                      Accuracy and Stability of Numerical Algorithms\n                      , 2nd ed., SIAM, Philadelphia, 2002,https:\/\/doi.org\/10.1137\/1.9780898718027.","DOI":"10.1137\/1.9780898718027"},{"key":"atypb24","doi-asserted-by":"crossref","unstructured":"N. J. Higham,\n                      Functions of Matrices: Theory and Computation\n                      , SIAM, Philadelphia, 2008,https:\/\/doi.org\/10.1137\/1.9780898717778.","DOI":"10.1137\/1.9780898717778"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1007\/BF02289026"},{"key":"atypb26","doi-asserted-by":"crossref","unstructured":"J. C. Mason and D. C. 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Trefethen,\n                      Approximation Theory and Approximation Practice\n                      , SIAM, Philadelphia, 2013."},{"key":"atypb32","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2010.06.034"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1191786","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:47:30Z","timestamp":1787327250000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1191786"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":32,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/18M1191786"],"URL":"https:\/\/doi.org\/10.1137\/18m1191786","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}