{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,30]],"date-time":"2025-05-30T04:05:54Z","timestamp":1748577954969,"version":"3.41.0"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,4,22]],"date-time":"2025-04-22T00:00:00Z","timestamp":1745280000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,4,22]],"date-time":"2025-04-22T00:00:00Z","timestamp":1745280000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2025,6]]},"DOI":"10.1007\/s00211-025-01466-7","type":"journal-article","created":{"date-parts":[[2025,4,22]],"date-time":"2025-04-22T15:13:29Z","timestamp":1745334809000},"page":"897-949","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A CJ-FEAST GSVDsolver for computing a partial GSVD of a large matrix pair with the generalized singular values in a given interval"],"prefix":"10.1007","volume":"157","author":[{"given":"Zhongxiao","family":"Jia","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kailiang","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,4,22]]},"reference":[{"key":"1466_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2023.115506","author":"F Alvarruiz","year":"2023","unstructured":"Alvarruiz, F., Campos, C., Roman, J.E.: Thick-restarted joint Lanczos bidiagonalization for the GSVD. J. Comput. Appl. Math. (2023). https:\/\/doi.org\/10.1016\/j.cam.2023.115506","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"1466_CR2","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1145\/1944345.1944349","volume":"58","author":"H Avron","year":"2011","unstructured":"Avron, H., Toledo, S.: Randomized algorithms for estimating the trace of an implicit symmetric positive semi-definite matrix. J. ACM 58(2), 17 (2011). https:\/\/doi.org\/10.1145\/1944345.1944349","journal-title":"J. ACM"},{"key":"1466_CR3","doi-asserted-by":"publisher","unstructured":"Bj\u00f6rck, A.: Numerical Methods for Least Squares Problems. SIAM, Philadelphia, PA (1996). https:\/\/doi.org\/10.1137\/1.9781611971484","DOI":"10.1137\/1.9781611971484"},{"issue":"3","key":"1466_CR4","doi-asserted-by":"publisher","first-page":"875","DOI":"10.1007\/s10208-021-09525-9","volume":"22","author":"A Cortinovis","year":"2022","unstructured":"Cortinovis, A., Kressner, D.: On randomized trace estimates for indefinite matrices with an application to determinants. Found. Comput. Math. 22(3), 875\u2013903 (2022). https:\/\/doi.org\/10.1007\/s10208-021-09525-9","journal-title":"Found. Comput. Math."},{"key":"1466_CR5","doi-asserted-by":"publisher","unstructured":"Davis, T.A., Hu, Y.: The University of Florida sparse matrix collection. ACM Trans. Math. Softw. 38(1), Art. 1, 25 (2011). https:\/\/doi.org\/10.1145\/2049662.2049663","DOI":"10.1145\/2049662.2049663"},{"key":"1466_CR6","unstructured":"Futamura, Y., Sakurai, T.: z-Pares: Parallel Eigenvalue Solver (2014). https:\/\/zpares.cs.tsukuba.ac.jp\/"},{"issue":"5","key":"1466_CR7","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2188","volume":"25","author":"B Gavin","year":"2018","unstructured":"Gavin, B., Polizzi, E.: Krylov eigenvalue strategy using the FEAST algorithm with inexact system solves. Numer. Linear Algebra Appl. 25(5), e2188 (2018). https:\/\/doi.org\/10.1002\/nla.2188","journal-title":"Numer. Linear Algebra Appl."},{"key":"1466_CR8","doi-asserted-by":"publisher","DOI":"10.56021\/9781421407944","volume-title":"Matrix Computations","author":"GH Golub","year":"2013","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computations, 4th edn. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, Baltimore, MD (2013)","edition":"4"},{"issue":"4","key":"1466_CR9","doi-asserted-by":"publisher","first-page":"A2100","DOI":"10.1137\/140980090","volume":"37","author":"S G\u00fcttel","year":"2015","unstructured":"G\u00fcttel, S., Polizzi, E., Tang, P., Viaud, G.: Zolotarev quadrature rules and load balancing for the FEAST eigensolver. SIAM J. Sci. Comput. 37(4), A2100\u2013A2122 (2015). https:\/\/doi.org\/10.1137\/140980090","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"1466_CR10","doi-asserted-by":"publisher","first-page":"491","DOI":"10.1007\/BF02219234","volume":"29","author":"PC Hansen","year":"1989","unstructured":"Hansen, P.C.: Regularization, GSVD and truncated GSVD. BIT 29(3), 491\u2013504 (1989). https:\/\/doi.org\/10.1007\/BF02219234","journal-title":"BIT"},{"key":"1466_CR11","doi-asserted-by":"publisher","unstructured":"Hansen, P.C.: Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion. SIAM, Philadelphia, PA (1998). https:\/\/doi.org\/10.1137\/1.9780898719697","DOI":"10.1137\/1.9780898719697"},{"issue":"3\u20134","key":"1466_CR12","doi-asserted-by":"publisher","first-page":"471","DOI":"10.1016\/j.laa.2009.03.003","volume":"431","author":"ME Hochstenbach","year":"2009","unstructured":"Hochstenbach, M.E.: A Jacobi\u2013Davidson type method for the generalized singular value problem. Linear Algebra Appl. 431(3\u20134), 471\u2013487 (2009). https:\/\/doi.org\/10.1016\/j.laa.2009.03.003","journal-title":"Linear Algebra Appl."},{"issue":"2","key":"1466_CR13","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1007\/s11075-020-00984-9","volume":"87","author":"J Huang","year":"2021","unstructured":"Huang, J., Jia, Z.: On choices of formulations of computing the generalized singular value decomposition of a large matrix pair. Numer. Algor. 87(2), 689\u2013718 (2021). https:\/\/doi.org\/10.1007\/s11075-020-00984-9","journal-title":"Numer. Algor."},{"key":"1466_CR14","doi-asserted-by":"publisher","unstructured":"Huang, J., Jia, Z.: Two harmonic Jacobi\u2013Davidson methods for computing a partial generalized singular value decomposition of a large matrix pair. J. Sci. Comput. 93 (2022), Paper no.41 https:\/\/doi.org\/10.1007\/s10915-022-01993-7. Paper no.41","DOI":"10.1007\/s10915-022-01993-7"},{"key":"1466_CR15","doi-asserted-by":"publisher","unstructured":"Huang, J., Jia, Z.: A cross-product free Jacobi\u2013Davidson type method for computing a partial generalized singular value decomposition of a large matrix pair. J. Sci. Comput. 94 (2023), Paper no.3https:\/\/doi.org\/10.1007\/s10915-022-02053-w10.1007","DOI":"10.1007\/s10915-022-02053-w10.1007"},{"key":"1466_CR16","doi-asserted-by":"publisher","unstructured":"Huang, J., Jia, Z.: Refined and refined harmonic Jacobi\u2013Davidson methods for computing several GSVD components of a large regular matrix pair. Numer. Algor. https:\/\/doi.org\/10.1007\/s11075-024-01901-0","DOI":"10.1007\/s11075-024-01901-0"},{"issue":"8","key":"1466_CR17","doi-asserted-by":"publisher","first-page":"1927","DOI":"10.1016\/j.cam.2009.09.029","volume":"233","author":"T Ikegami","year":"2010","unstructured":"Ikegami, T., Sakurai, T., Nagashima, U.: A filter diagonalization for generalized eigenvalue problems based on the Sakurai\u2013Sugiura projection method. J. Comput. Appl. Math. 233(8), 1927\u20131936 (2010). https:\/\/doi.org\/10.1016\/j.cam.2009.09.029","journal-title":"J. Comput. Appl. Math."},{"key":"1466_CR18","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/j.aml.2014.02.007","volume":"32","author":"A Imakura","year":"2014","unstructured":"Imakura, A., Du, L., Sakurai, T.: A block Arnoldi-type contour integral spectral projection method for solving generalized eigenvalue problems. Appl. Math. Lett. 32, 22\u201327 (2014). https:\/\/doi.org\/10.1016\/j.aml.2014.02.007","journal-title":"Appl. Math. Lett."},{"issue":"3","key":"1466_CR19","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1007\/s13160-016-0224-x","volume":"33","author":"A Imakura","year":"2016","unstructured":"Imakura, A., Du, L., Sakurai, T.: Relationships among contour integral-based methods for solving generalized eigenvalue problems. Jpn. J. Ind. Appl. Math. 33(3), 721\u2013750 (2016). https:\/\/doi.org\/10.1007\/s13160-016-0224-x","journal-title":"Jpn. J. Ind. Appl. Math."},{"key":"1466_CR20","doi-asserted-by":"publisher","unstructured":"Imakura, A., Sakurai, T.: Complex moment-based method with nonlinear transformation for computing large and sparse interior singular triplets (2021) https:\/\/doi.org\/10.48550\/arXiv.2109.13655","DOI":"10.48550\/arXiv.2109.13655"},{"issue":"1","key":"1466_CR21","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/S0010-4655(98)00192-1","volume":"118","author":"LO Jay","year":"1999","unstructured":"Jay, L.O., Kim, H., Saad, Y., Chelikowsky, J.R.: Electronic structure calculations for plane-wave codes without diagonalization. Comput. Phys. Commun. 118(1), 21\u201330 (1999). https:\/\/doi.org\/10.1016\/S0010-4655(98)00192-1","journal-title":"Comput. Phys. Commun."},{"issue":"2","key":"1466_CR22","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1007\/s11075-020-01064-8","volume":"88","author":"Z Jia","year":"2021","unstructured":"Jia, Z., Li, H.: The joint bidiagonalization process with partial reorthogonalization. Numer. Algor. 88(2), 965\u2013992 (2021). https:\/\/doi.org\/10.1007\/s11075-020-01064-8","journal-title":"Numer. Algor."},{"issue":"1","key":"1466_CR23","doi-asserted-by":"publisher","first-page":"382","DOI":"10.1137\/22M1483608","volume":"44","author":"Z Jia","year":"2023","unstructured":"Jia, Z., Li, H.: The joint bidiagonalization method for large GSVD computations in finite precision. SIAM J. Matrix Anal. Appl. 44(1), 382\u2013407 (2023). https:\/\/doi.org\/10.1137\/22M1483608","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"1466_CR24","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1016\/j.apnum.2020.06.001","volume":"157","author":"Z Jia","year":"2020","unstructured":"Jia, Z., Yang, Y.: A joint bidiagonalization based iterative algorithm for large scale general-form Tikhonov regularization. Appl. Numer. Math. 157, 159\u2013177 (2020). https:\/\/doi.org\/10.1016\/j.apnum.2020.06.001","journal-title":"Appl. Numer. Math."},{"key":"1466_CR25","doi-asserted-by":"publisher","unstructured":"Jia, Z., Zhang, K.: A FEAST SVDsolver based on Chebyshev\u2013Jackson series for computing partial singular triplets of large matrices. J. Sci. Comput. 97 (2023), Paper no.21. https:\/\/doi.org\/10.1007\/s10915-023-02342-y","DOI":"10.1007\/s10915-023-02342-y"},{"key":"1466_CR26","doi-asserted-by":"publisher","unstructured":"Jia, Z., Zhang, K.: An augmented matrix-based CJ-FEAST SVDsolver for computing a partial singular value decomposition with the singular values in a given interval. SIAM J. Matrix Anal. Appl. 45, 24\u201358 (2024). https:\/\/doi.org\/10.1137\/23M1547500","DOI":"10.1137\/23M1547500"},{"issue":"5","key":"1466_CR27","doi-asserted-by":"publisher","first-page":"S772","DOI":"10.1137\/15M1026572","volume":"38","author":"J Kestyn","year":"2016","unstructured":"Kestyn, J., Polizzi, E., Tang, P.: FEAST eigensolver for non-Hermitian problems. SIAM J. Sci. Comput. 38(5), S772\u2013S799 (2016). https:\/\/doi.org\/10.1137\/15M1026572","journal-title":"SIAM J. Sci. Comput."},{"issue":"1","key":"1466_CR28","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1137\/050645592","volume":"29","author":"ME Kilmer","year":"2007","unstructured":"Kilmer, M.E., Hansen, P.C., Espanol, M.I.: A projection-based approach to general-form Tikhonov regularization. SIAM J. Sci. Comput. 29(1), 315\u2013330 (2007)","journal-title":"SIAM J. Sci. Comput."},{"issue":"4","key":"1466_CR29","doi-asserted-by":"publisher","first-page":"A2660","DOI":"10.1137\/20M1313933","volume":"43","author":"K Kollnig","year":"2021","unstructured":"Kollnig, K., Bientinesi, P., Di Napoli, E.A.: Rational spectral filters with optimal convergence rate. SIAM J. Sci. Comput. 43(4), A2660\u2013A2684 (2021). https:\/\/doi.org\/10.1137\/20M1313933","journal-title":"SIAM J. Sci. Comput."},{"issue":"3","key":"1466_CR30","doi-asserted-by":"publisher","first-page":"398","DOI":"10.1137\/0718026","volume":"18","author":"CC Paige","year":"1981","unstructured":"Paige, C.C., Saunders, M.A.: Towards a generalized singular value decomposition. SIAM J. Numer. Anal. 18(3), 398\u2013405 (1981). https:\/\/doi.org\/10.1137\/0718026","journal-title":"SIAM J. Numer. Anal."},{"key":"1466_CR31","doi-asserted-by":"publisher","unstructured":"Parlett, B.N.: The Symmetric Eigenvalue Problem, Classics in Applied Mathematics, vol.\u00a020. SIAM, Philadelphia, PA (1998). https:\/\/doi.org\/10.1137\/1.9781611971163","DOI":"10.1137\/1.9781611971163"},{"key":"1466_CR32","doi-asserted-by":"publisher","unstructured":"Polizzi, E.: Density-matrix-based algorithm for solving eigenvalue problems. Phys. Rev. B 79(11), e115112, 6 (2009). https:\/\/doi.org\/10.1103\/PhysRevB.79.115112","DOI":"10.1103\/PhysRevB.79.115112"},{"key":"1466_CR33","doi-asserted-by":"publisher","unstructured":"Polizzi, E.: FEAST eigenvalue solver v4.0 user guide (2020).https:\/\/doi.org\/10.48550\/arXiv.2002.04807","DOI":"10.48550\/arXiv.2002.04807"},{"key":"1466_CR34","volume-title":"An Introduction to the Approximation of Functions","author":"TJ Rivlin","year":"1981","unstructured":"Rivlin, T.J.: An Introduction to the Approximation of Functions. Dover Books on Advanced Mathematics. Dover Publications Inc, New York (1981)"},{"issue":"5","key":"1466_CR35","doi-asserted-by":"publisher","first-page":"1535","DOI":"10.1137\/S1064827595285597","volume":"19","author":"A Ruhe","year":"1998","unstructured":"Ruhe, A.: Rational Krylov: a practical algorithm for large sparse nonsymmetric matrix pencils. SIAM J. Sci. Comput. 19(5), 1535\u20131551 (1998). https:\/\/doi.org\/10.1137\/S1064827595285597","journal-title":"SIAM J. Sci. Comput."},{"key":"1466_CR36","doi-asserted-by":"publisher","unstructured":"Saad, Y.: Iterative Methods for Sparse Linear Systems, second edn. SIAM, Philadelphia, PA (2003). https:\/\/doi.org\/10.1137\/1.9780898718003","DOI":"10.1137\/1.9780898718003"},{"key":"1466_CR37","doi-asserted-by":"publisher","unstructured":"Saad, Y.: Numerical Methods for Large Eigenvalue Problems, Classics in Applied Mathematics, vol.\u00a066. SIAM, Philadelphia, PA (2011). https:\/\/doi.org\/10.1137\/1.9781611970739","DOI":"10.1137\/1.9781611970739"},{"issue":"1","key":"1466_CR38","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1016\/S0377-0427(03)00565-X","volume":"159","author":"T Sakurai","year":"2003","unstructured":"Sakurai, T., Sugiura, H.: A projection method for generalized eigenvalue problems using numerical integration. J. Comput. Appl. Math. 159(1), 119\u2013128 (2003). https:\/\/doi.org\/10.1016\/S0377-0427(03)00565-X","journal-title":"J. Comput. Appl. Math."},{"issue":"4","key":"1466_CR39","doi-asserted-by":"publisher","first-page":"745","DOI":"10.14492\/hokmj\/1272848031","volume":"36","author":"T Sakurai","year":"2007","unstructured":"Sakurai, T., Tadano, H.: CIRR: a Rayleigh\u2013Ritz type method with contour integral for generalized eigenvalue problems. Hokkaido Math. J. 36(4), 745\u2013757 (2007). https:\/\/doi.org\/10.14492\/hokmj\/1272848031","journal-title":"Hokkaido Math. J."},{"key":"1466_CR40","doi-asserted-by":"publisher","unstructured":"Stewart, G.W.: Matrix Algorithms, Vol. I: Basic Decompositions. SIAM, Philadelphia, PA (1998). https:\/\/doi.org\/10.1137\/1.9781611971408","DOI":"10.1137\/1.9781611971408"},{"key":"1466_CR41","doi-asserted-by":"publisher","unstructured":"Stewart, G.W.: Matrix Algorithms, Vol. II: Eigensystems. SIAM, Philadelphia, PA (2001). https:\/\/doi.org\/10.1137\/1.9780898718058","DOI":"10.1137\/1.9780898718058"},{"key":"1466_CR42","volume-title":"Matrix Perturbation Theory","author":"GW Stewart","year":"1990","unstructured":"Stewart, G.W., Sun, J.-G.: Matrix Perturbation Theory. Academic Press, London (1990)"},{"issue":"2","key":"1466_CR43","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1137\/13090866X","volume":"35","author":"P Tang","year":"2014","unstructured":"Tang, P., Polizzi, E.: FEAST as a subspace iteration eigensolver accelerated by approximate spectral projection. SIAM J. Matrix Anal. Appl. 35(2), 354\u2013390 (2014). https:\/\/doi.org\/10.1137\/13090866X","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"1466_CR44","doi-asserted-by":"publisher","unstructured":"Van\u00a0Huffel, S., Lemmerling, P. (eds.): Total Least Squares and Errors-in-Variables Modeling: Analysis, Algorithms and Applications. Kluwer Academic Publishers, Dordrecht (2002). https:\/\/doi.org\/10.1007\/978-94-017-3552-0","DOI":"10.1007\/978-94-017-3552-0"},{"issue":"1","key":"1466_CR45","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1137\/0713009","volume":"13","author":"CF Van Loan","year":"1976","unstructured":"Van Loan, C.F.: Generalizing the singular value decomposition. SIAM J. Numer. Anal. 13(1), 76\u201383 (1976). https:\/\/doi.org\/10.1137\/0713009","journal-title":"SIAM J. Numer. Anal."},{"issue":"3","key":"1466_CR46","doi-asserted-by":"publisher","first-page":"391","DOI":"10.1007\/s002110050175","volume":"72","author":"H Zha","year":"1996","unstructured":"Zha, H.: Computing the generalized singular values\/vectors of large sparse or structured matrix pairs. Numer. Math. 72(3), 391\u2013417 (1996). https:\/\/doi.org\/10.1007\/s002110050175","journal-title":"Numer. Math."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-025-01466-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00211-025-01466-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-025-01466-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,29]],"date-time":"2025-05-29T10:57:47Z","timestamp":1748516267000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00211-025-01466-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,22]]},"references-count":46,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["1466"],"URL":"https:\/\/doi.org\/10.1007\/s00211-025-01466-7","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"type":"print","value":"0029-599X"},{"type":"electronic","value":"0945-3245"}],"subject":[],"published":{"date-parts":[[2025,4,22]]},"assertion":[{"value":"4 November 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 December 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 March 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 April 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The two authors declare that they have no financial interests, and they read and approved the final manuscript.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}