{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:55:16Z","timestamp":1776848116044,"version":"3.51.2"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2013,12,12]],"date-time":"2013-12-12T00:00:00Z","timestamp":1386806400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2014,8]]},"DOI":"10.1007\/s00211-013-0600-2","type":"journal-article","created":{"date-parts":[[2013,12,11]],"date-time":"2013-12-11T10:48:51Z","timestamp":1386758931000},"page":"751-799","source":"Crossref","is-referenced-by-count":55,"title":["On the spectrum of stiffness matrices arising from isogeometric analysis"],"prefix":"10.1007","volume":"127","author":[{"given":"Carlo","family":"Garoni","sequence":"first","affiliation":[]},{"given":"Carla","family":"Manni","sequence":"additional","affiliation":[]},{"given":"Francesca","family":"Pelosi","sequence":"additional","affiliation":[]},{"given":"Stefano","family":"Serra-Capizzano","sequence":"additional","affiliation":[]},{"given":"Hendrik","family":"Speleers","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,12,12]]},"reference":[{"key":"600_CR1","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1137\/S0895479803421987","volume":"26","author":"A Aric\u00f3","year":"2004","unstructured":"Aric\u00f3, A., Donatelli, M., Serra-Capizzano, S.: V-cycle optimal convergence for certain (multilevel) structured linear systems. SIAM J. Matrix Anal. Appl. 26, 186\u2013214 (2004)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"600_CR2","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1007\/BF01389448","volume":"48","author":"O Axelsson","year":"1986","unstructured":"Axelsson, O., Lindskog, G.: On the rate of convergence of the preconditioned conjugate gradient method. Numer. Math. 48, 499\u2013523 (1986)","journal-title":"Numer. Math."},{"key":"600_CR3","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.cma.2009.02.036","volume":"199","author":"Y Bazilevs","year":"2010","unstructured":"Bazilevs, Y., Calo, V.M., Cottrell, J.A., Evans, J.A., Hughes, T.J.R., Lipton, S., Scott, M.A., Sederberg, T.W.: Isogeometric analysis using T-splines. Comput. Methods Appl. Mech. Eng. 199, 229\u2013263 (2010)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"600_CR4","doi-asserted-by":"crossref","first-page":"300","DOI":"10.1137\/S0036142999363188","volume":"39","author":"B Beckermann","year":"2001","unstructured":"Beckermann, B., Kuijlaars, A.B.J.: Superlinear convergence of Conjugate Gradients. SIAM J. Numer. Anal. 39, 300\u2013329 (2001)","journal-title":"SIAM J. Numer. Anal."},{"key":"600_CR5","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1023\/A:1021964506568","volume":"41","author":"B Beckermann","year":"2001","unstructured":"Beckermann, B., Kuijlaars, A.B.J.: On the sharpness of an asymptotic error estimate for Conjugate Gradients. BIT 41, 856\u2013867 (2001)","journal-title":"BIT"},{"key":"600_CR6","doi-asserted-by":"crossref","first-page":"746","DOI":"10.1137\/05063533X","volume":"45","author":"B Beckermann","year":"2007","unstructured":"Beckermann, B., Serra-Capizzano, S.: On the asymptotic spectrum of Finite Elements matrices. SIAM J. Numer. Anal. 45, 746\u2013769 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"600_CR7","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1007\/s00211-004-0574-1","volume":"99","author":"D Bertaccini","year":"2005","unstructured":"Bertaccini, D., Golub, G., Serra-Capizzano, S., Tablino Possio, C.: Preconditioned HSS method for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection\u2013diffusion equation. Numer. Math. 99, 441\u2013484 (2005)","journal-title":"Numer. Math."},{"key":"600_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0653-8","volume-title":"Matrix Analysis","author":"R Bhatia","year":"1997","unstructured":"Bhatia, R.: Matrix Analysis. Springer, New York (1997)"},{"key":"600_CR9","volume-title":"A Practical Guide to Splines","author":"C Boor de","year":"2001","unstructured":"de Boor, C.: A Practical Guide to Splines. Springer, New York (2001)"},{"key":"600_CR10","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-1426-7","volume-title":"Introduction to Large Truncated Toeplitz Matrices","author":"A B\u00f6ttcher","year":"1999","unstructured":"B\u00f6ttcher, A., Silbermann, B.: Introduction to Large Truncated Toeplitz Matrices. Springer, New York (1999)"},{"key":"600_CR11","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/978-3-7643-7980-3_4","volume":"171","author":"A B\u00f6ttcher","year":"2007","unstructured":"B\u00f6ttcher, A., Widom, H.: From Toeplitz eigenvalues through Green\u2019s kernels to higher-order Wirtinger\u2013Sobolev inequalities. Oper. Theory Adv. Appl. 171, 73\u201387 (2007)","journal-title":"Oper. Theory Adv. Appl."},{"key":"600_CR12","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.cma.2013.05.014","volume":"265","author":"A Buffa","year":"2013","unstructured":"Buffa, A., Harbrecht, H., Kunoth, A., Sangalli, G.: BPX-preconditioning for isogeometric analysis. Comput. Methods Appl. Mech. Eng. 265, 63\u201370 (2013)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"600_CR13","volume-title":"An Introduction to Wavelets","author":"CK Chui","year":"1992","unstructured":"Chui, C.K.: An Introduction to Wavelets. Academic Press, San Diego (1992)"},{"key":"600_CR14","doi-asserted-by":"crossref","DOI":"10.1002\/9780470749081","volume-title":"Isogeometric Analysis: Toward Integration of CAD and FEA","author":"JA Cottrell","year":"2009","unstructured":"Cottrell, J.A., Hughes, T.J.R., Bazilevs, Y.: Isogeometric Analysis: Toward Integration of CAD and FEA. Wiley, Chichester (2009)"},{"key":"600_CR15","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/j.cma.2012.08.015","volume":"253","author":"KPS Gahalaut","year":"2013","unstructured":"Gahalaut, K.P.S., Kraus, J.K., Tomar, S.K.: Multigrid methods for isogeometric discretization. Comput. Methods Appl. Mech. Eng. 253, 413\u2013425 (2013)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"600_CR16","doi-asserted-by":"crossref","unstructured":"Garoni, C., Manni, C., Pelosi, F., Serra-Capizzano, S., Speleers, H.: On the spectrum of stiffness matrices arising from isogeometric analysis. Technical Report TW632, Department of Computer Science, KU Leuven (2013)","DOI":"10.1007\/s00211-013-0600-2"},{"key":"600_CR17","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.jat.2006.05.002","volume":"144","author":"L Golinskii","year":"2007","unstructured":"Golinskii, L., Serra-Capizzano, S.: The asymptotic properties of the spectrum of nonsymmetrically perturbed Jacobi matrix sequences. J. Approx. Theory 144, 84\u2013102 (2007)","journal-title":"J. Approx. Theory"},{"key":"600_CR18","volume-title":"Toeplitz Forms and Their Applications","author":"U Grenander","year":"1984","unstructured":"Grenander, U., Szeg\u00f6, G.: Toeplitz Forms and Their Applications, 2nd edn. Chelsea, New York (1984)","edition":"2"},{"key":"600_CR19","doi-asserted-by":"crossref","first-page":"129","DOI":"10.2307\/1970473","volume":"2","author":"L H\u00f6rmander","year":"1966","unstructured":"H\u00f6rmander, L.: Pseudo-differential operators and non-elliptic boundary problems. Ann. Math. 2, 129\u2013209 (1966)","journal-title":"Ann. Math."},{"key":"600_CR20","doi-asserted-by":"crossref","first-page":"4135","DOI":"10.1016\/j.cma.2004.10.008","volume":"194","author":"TJR Hughes","year":"2005","unstructured":"Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Comput. Methods Appl. Mech. Eng. 194, 4135\u20134195 (2005)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"600_CR21","doi-asserted-by":"crossref","first-page":"867","DOI":"10.1016\/j.cma.2010.10.010","volume":"200","author":"C Manni","year":"2011","unstructured":"Manni, C., Pelosi, F., Sampoli, M.L.: Generalized B-splines as a tool in isogeometric analysis. Comput. Methods Appl. Mech. Eng. 200, 867\u2013881 (2011)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"600_CR22","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1090\/S0002-9904-1961-10563-6","volume":"67","author":"SV Parter","year":"1961","unstructured":"Parter, S.V.: On the extreme eigenvalues of truncated Toeplitz matrices. Bull. Am. Math. Soc. 67, 191\u2013197 (1961)","journal-title":"Bull. Am. Math. Soc."},{"key":"600_CR23","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1007\/BF00253939","volume":"3","author":"SV Parter","year":"1962","unstructured":"Parter, S.V.: On the eigenvalues of certain generalizations of Toeplitz matrices. Arch. Ration. Math. Mech. 3, 244\u2013257 (1962)","journal-title":"Arch. Ration. Math. Mech."},{"key":"600_CR24","doi-asserted-by":"crossref","DOI":"10.1007\/978-88-470-1071-0","volume-title":"Numerical Models for Differential Problems","author":"A Quarteroni","year":"2009","unstructured":"Quarteroni, A.: Numerical Models for Differential Problems. Springer, Italy (2009)"},{"key":"600_CR25","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1137\/080730974","volume":"31","author":"A Russo","year":"2009","unstructured":"Russo, A., Tablino Possio, C.: Preconditioned Hermitian and skew-Hermitian splitting method for finite element approximations of convection\u2013diffusion equations. SIAM J. Matrix Anal. Appl. 31, 997\u20131018 (2009)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"600_CR26","volume-title":"Iterative Methods for Sparse Linear Systems","author":"Y Saad","year":"1996","unstructured":"Saad, Y.: Iterative Methods for Sparse Linear Systems. PWS Publishing, Boston (1996)"},{"key":"600_CR27","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511618994","volume-title":"Spline Functions: Basic Theory","author":"LL Schumaker","year":"2007","unstructured":"Schumaker, L.L.: Spline Functions: Basic Theory, 3rd edn. Cambridge Mathematical Library, Cambridge (2007)","edition":"3"},{"key":"600_CR28","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1007\/BF01934269","volume":"34","author":"S Serra-Capizzano","year":"1994","unstructured":"Serra-Capizzano, S.: Preconditioning strategies for asymptotically ill-conditioned block Toeplitz systems. BIT 34, 579\u2013594 (1994)","journal-title":"BIT"},{"key":"600_CR29","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/S0024-3795(02)00504-9","volume":"366","author":"S Serra-Capizzano","year":"2003","unstructured":"Serra-Capizzano, S.: Generalized Locally Toeplitz sequences: spectral analysis and applications to discretized partial differential equations. Linear Algebra Appl. 366, 371\u2013402 (2003)","journal-title":"Linear Algebra Appl."},{"key":"600_CR30","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.laa.2006.04.012","volume":"419","author":"S Serra-Capizzano","year":"2006","unstructured":"Serra-Capizzano, S.: GLT sequences as a generalized Fourier analysis and applications. Linear Algebra Appl. 419, 180\u2013233 (2006)","journal-title":"Linear Algebra Appl."},{"key":"600_CR31","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/S0024-3795(99)00022-1","volume":"293","author":"S Serra-Capizzano","year":"1999","unstructured":"Serra-Capizzano, S., Tablino Possio, C.: Spectral and structural analysis of high precision finite difference matrices for elliptic operators. Linear Algebra Appl. 293, 85\u2013131 (1999)","journal-title":"Linear Algebra Appl."},{"key":"600_CR32","volume-title":"Numerical Solution of Partial Differential Equations: Finite Difference Methods","author":"GD Smith","year":"1985","unstructured":"Smith, G.D.: Numerical Solution of Partial Differential Equations: Finite Difference Methods, 3rd edn. Clarendon Press, Oxford (1985)","edition":"3"},{"key":"600_CR33","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.cma.2012.02.009","volume":"221\u2013222","author":"H Speleers","year":"2012","unstructured":"Speleers, H., Manni, C., Pelosi, F., Sampoli, M.L.: Isogeometric analysis with Powell\u2013Sabin splines for advection\u2013diffusion\u2013reaction problems. Comput. Methods Appl. Mech. Eng. 221\u2013222, 132\u2013148 (2012)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"600_CR34","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1080\/03081089808818584","volume":"45","author":"P Tilli","year":"1998","unstructured":"Tilli, P.: A note on the spectral distribution of Toeplitz matrices. Linear Multilinear Algebra 45, 147\u2013159 (1998)","journal-title":"Linear Multilinear Algebra"},{"key":"600_CR35","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/S0024-3795(97)10079-9","volume":"278","author":"P Tilli","year":"1998","unstructured":"Tilli, P.: Locally Toeplitz sequences: spectral properties and applications. Linear Algebra Appl. 278, 91\u2013120 (1998)","journal-title":"Linear Algebra Appl."},{"key":"600_CR36","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1007\/BF01389450","volume":"48","author":"A Sluis van der","year":"1986","unstructured":"van der Sluis, A., van der Vorst, H.A.: The rate of convergence of conjugate gradients. Numer. Math. 48, 543\u2013560 (1986)","journal-title":"Numer. Math."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-013-0600-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-013-0600-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-013-0600-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,4]],"date-time":"2019-08-04T19:56:31Z","timestamp":1564948591000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-013-0600-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12,12]]},"references-count":36,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,8]]}},"alternative-id":["600"],"URL":"https:\/\/doi.org\/10.1007\/s00211-013-0600-2","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12,12]]}}}