{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T12:07:12Z","timestamp":1759838832551},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2016,7,30]],"date-time":"2016-07-30T00:00:00Z","timestamp":1469836800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2017,4]]},"DOI":"10.1007\/s00211-016-0831-0","type":"journal-article","created":{"date-parts":[[2016,7,30]],"date-time":"2016-07-30T10:53:30Z","timestamp":1469876010000},"page":"1253-1287","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Quadratic convergence of approximations by CCC-Schoenberg operators"],"prefix":"10.1007","volume":"135","author":[{"given":"Tina","family":"Bosner","sequence":"first","affiliation":[]},{"given":"Mladen","family":"Rogina","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,7,30]]},"reference":[{"key":"831_CR1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00211-009-0248-0","volume":"114","author":"JM Aldaz","year":"2009","unstructured":"Aldaz, J.M., Kounchev, O., Render, H.: Shape preserving properties of generalized Bernstein operators on extended Chebyshev spaces. Numer. Math. 114, 1\u201325 (2009)","journal-title":"Numer. Math."},{"key":"831_CR2","first-page":"35","volume-title":"Curve and Surfaces in Geometric Design","author":"D Bister","year":"1997","unstructured":"Bister, D., Prautzsch, H.: A new approach to Tchebycheffian B-splines. In: M\u00e9haute\u00e9, A.L., Rabut, C., Schumaker, L.L. (eds.) Curve and Surfaces in Geometric Design, pp. 35\u201343. Vanderbilt University Press, Nashville (1997)"},{"key":"831_CR3","doi-asserted-by":"crossref","unstructured":"Bosner, T.: Knot insertion algorithms for weighted splines. In: Drma\u010d, Z., Maru\u0161i\u0107, M., Tutek, Z. (eds.) Proceedings of the Conference on Applied Mathematics and Scientific Computing, pp. 151\u2013160. Springer, Berlin (2005)","DOI":"10.1007\/1-4020-3197-1_9"},{"key":"831_CR4","unstructured":"Bosner, T.: Knot insertion algorithms for Chebyshev splines. Ph.D. thesis, Dept. of Mathematics, University of Zagreb (2006). http:\/\/web.math.hr\/~tinab\/TinaBosnerPhD.pdf"},{"issue":"1","key":"831_CR5","first-page":"1","volume":"15","author":"T Bosner","year":"2010","unstructured":"Bosner, T.: Basis of splines associated with singularly perturbed advection-diffusion problems. Math. Commun. 15(1), 1\u201312 (2010)","journal-title":"Math. Commun."},{"key":"831_CR6","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1007\/s11075-007-9138-7","volume":"46","author":"T Bosner","year":"2007","unstructured":"Bosner, T., Rogina, M.: Non-uniform exponential tension splines. Numer. Algor. 46, 265\u2013294 (2007)","journal-title":"Numer. Algor."},{"issue":"2","key":"831_CR7","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1007\/s11565-008-0045-1","volume":"54","author":"T Bosner","year":"2008","unstructured":"Bosner, T., Rogina, M.: Collocation by singular splines. Annali dell\u2019Universit\u00e0 di Ferrara 54(2), 217\u2013227 (2008)","journal-title":"Annali dell\u2019Universit\u00e0 di Ferrara"},{"key":"831_CR8","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1007\/s10444-011-9242-z","volume":"38","author":"T Bosner","year":"2013","unstructured":"Bosner, T., Rogina, M.: Variable degree polynomial splines are Chebyshev splines. Adv. Comput. Math. 38, 383\u2013400 (2013)","journal-title":"Adv. Comput. Math."},{"key":"831_CR9","volume-title":"Measure, Integration, and Probability","author":"CW Burrill","year":"1972","unstructured":"Burrill, C.W.: Measure, Integration, and Probability. McGraw-Hill Book Company, New York (1972)"},{"key":"831_CR10","volume-title":"A Practical Guide to Splines, revised edition","author":"C Boor de","year":"2001","unstructured":"de Boor, C.: A Practical Guide to Splines, revised edition. Springer, Berlin (2001)"},{"key":"831_CR11","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.apnum.2004.04.002","volume":"52","author":"RW Johnson","year":"2005","unstructured":"Johnson, R.W.: Higher order B-spline collocation at the Greville abscissae. Appl. Numer. Math. 52, 63\u201375 (2005)","journal-title":"Appl. Numer. Math."},{"key":"831_CR12","volume-title":"Total Positivity","author":"S Karlin","year":"1968","unstructured":"Karlin, S.: Total Positivity. Stanford Univ. Press, California (1968)"},{"key":"831_CR13","volume-title":"Tchebycheff Systems: With Applications in Analysis and Statistics","author":"S Karlin","year":"1966","unstructured":"Karlin, S., Studden, W.: Tchebycheff Systems: With Applications in Analysis and Statistics. Wiley Interscience, New York (1966)"},{"issue":"10","key":"831_CR14","doi-asserted-by":"crossref","first-page":"2215","DOI":"10.1016\/j.matcom.2010.12.029","volume":"81","author":"I Kav\u010di\u010d","year":"2011","unstructured":"Kav\u010di\u010d, I., Rogina, M., Bosner, T.: Singularly perturbed advection-diffusion-reaction problems: comparison of operator-fitted methods. Math. Comput. Simul. 81(10), 2215\u20132224 (2011)","journal-title":"Math. Comput. Simul."},{"key":"831_CR15","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1007\/s00211-005-0617-2","volume":"101","author":"O Koch","year":"2005","unstructured":"Koch, O.: Asymptotically correct error estimation for collocation methods applied to singular boundary value problems. Numer. Math. 101, 143\u2013164 (2005)","journal-title":"Numer. Math."},{"issue":"1\u20133","key":"831_CR16","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1007\/s10444-004-7633-0","volume":"25","author":"T Lyche","year":"2006","unstructured":"Lyche, T., Mazure, M.L.: Total positivity and the existence of piecewise exponential B-splines. Adv. Comput. Math. 25(1\u20133), 105\u2013133 (2006)","journal-title":"Adv. Comput. Math."},{"key":"831_CR17","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/0021-9045(70)90058-4","volume":"3","author":"MJ Marsden","year":"1970","unstructured":"Marsden, M.J.: An identity for spline functions with applications to variation-diminishing spline approximation. J. Approx. Theory 3, 7\u201349 (1970)","journal-title":"J. Approx. Theory"},{"key":"831_CR18","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1007\/PL00005437","volume":"88","author":"M Maru\u0161i\u0107","year":"2001","unstructured":"Maru\u0161i\u0107, M.: A fourth\/second order accurate collocation method for singularly perturbed two-point boundary value problems using tension splines. Numer. Math. 88, 135\u2013158 (2001)","journal-title":"Numer. Math."},{"issue":"1","key":"831_CR19","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/BF02127696","volume":"6","author":"M Maru\u0161i\u0107","year":"1996","unstructured":"Maru\u0161i\u0107, M., Rogina, M.: A collocation method for singularly perturbed two-point boundary value problems with splines in tension. Adv. Comput. Math. 6(1), 65\u201376 (1996)","journal-title":"Adv. Comput. Math."},{"key":"831_CR20","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.jat.2004.06.004","volume":"131","author":"ML Mazure","year":"2004","unstructured":"Mazure, M.L.: Blossoms of generalized derivatives in Chebyshev spaces. J. Approx. Theory 131, 47\u201358 (2004)","journal-title":"J. Approx. Theory"},{"key":"831_CR21","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.jat.2006.06.008","volume":"143","author":"ML Mazure","year":"2006","unstructured":"Mazure, M.L.: On Chebyshevian spline subdivision. J. Approx. Theory 143, 74\u2013110 (2006)","journal-title":"J. Approx. Theory"},{"key":"831_CR22","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/s11075-008-9260-1","volume":"52","author":"ML Mazure","year":"2009","unstructured":"Mazure, M.L.: Bernstein-type operators in Chebyshev spaces. Numer. Algor. 52, 93\u2013128 (2009)","journal-title":"Numer. Algor."},{"key":"831_CR23","first-page":"111","volume":"1","author":"ML Mazure","year":"2009","unstructured":"Mazure, M.L.: On differentiation formulae for Chebyshevian Bernstein and B-spline bases. Ja\u00e9n J. Approx. 1, 111\u2013143 (2009)","journal-title":"Ja\u00e9n J. Approx."},{"key":"831_CR24","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/s00365-010-9123-6","volume":"34","author":"ML Mazure","year":"2011","unstructured":"Mazure, M.L.: Chebyshev\u2013Schoenberg operators. Constr. Approx. 34, 181\u2013208 (2011)","journal-title":"Constr. Approx."},{"key":"831_CR25","first-page":"67","volume":"3","author":"ML Mazure","year":"2011","unstructured":"Mazure, M.L.: A duality formula for chebyshevian divided differences and blossoms. Ja\u00e9n J. Approx. 3, 67\u201386 (2011)","journal-title":"Ja\u00e9n J. Approx."},{"key":"831_CR26","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.jat.2010.10.003","volume":"163","author":"ML Mazure","year":"2011","unstructured":"Mazure, M.L.: Finding all systems of weight functions associated with a given extended chebyshev space. J. Approx. Theory. 163, 363\u2013376 (2011)","journal-title":"J. Approx. Theory."},{"key":"831_CR27","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1007\/s00211-011-0390-3","volume":"119","author":"ML Mazure","year":"2011","unstructured":"Mazure, M.L.: How to build all Chebyshevian spline spaces good for geometric design? Numer. Math. 119, 517\u2013556 (2011)","journal-title":"Numer. Math."},{"key":"831_CR28","doi-asserted-by":"crossref","unstructured":"Mazure, M.L.: Quasi extended Chebyshev spaces and weight functions. Numer. Math. 118 (2011)","DOI":"10.1007\/s00211-010-0312-9"},{"key":"831_CR29","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.jat.2012.10.005","volume":"166","author":"ML Mazure","year":"2013","unstructured":"Mazure, M.L.: Piecewise Chebyshev\u2013Schoenberg operators: shape preservation, approximation and space embedding. J. Approx. Theory. 166, 106\u2013135 (2013)","journal-title":"J. Approx. Theory."},{"key":"831_CR30","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1006\/jath.1998.3306","volume":"98","author":"ML Mazure","year":"1999","unstructured":"Mazure, M.L., Laurent, P.J.: Piecewise smooth spaces in duality: application to blossoming. J. Approx. Theory 98, 316\u2013353 (1999)","journal-title":"J. Approx. Theory"},{"key":"831_CR31","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1007\/BF02074883","volume":"32","author":"M Rogina","year":"1992","unstructured":"Rogina, M.: Basis of splines associated with some singular differential operators. BIT 32, 496\u2013505 (1992)","journal-title":"BIT"},{"key":"831_CR32","first-page":"83","volume":"4","author":"M Rogina","year":"1999","unstructured":"Rogina, M.: On construction of fourth order Chebyshev splines. Math. Commun. 4, 83\u201392 (1999)","journal-title":"Math. Commun."},{"key":"831_CR33","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1007\/1-4020-3197-1_20","volume-title":"Proceedings of the Conference on Applied Mathematics and Scientific Computing","author":"M Rogina","year":"2005","unstructured":"Rogina, M.: Algebraic proof of the B-spline derivative formula. In: Drma\u010d, Z., Maru\u0161i\u0107, M., Tutek, Z. (eds.) Proceedings of the Conference on Applied Mathematics and Scientific Computing, pp. 273\u2013282. Springer, Berlin (2005)"},{"key":"831_CR34","first-page":"343","volume-title":"Curves and Surfaces Design","author":"M Rogina","year":"2000","unstructured":"Rogina, M., Bosner, T.: On calculating with lower order Chebyshev splines. In: Laurent, P.J., Sabloniere, P., Schumaker, L.L. (eds.) Curves and Surfaces Design, pp. 343\u2013353. Vanderbilt Univ. Press, Nashville (2000)"},{"key":"831_CR35","volume-title":"Real Analysis","author":"HL Royden","year":"2010","unstructured":"Royden, H.L., Fitzpatrick, P.M.: Real Analysis, 4th edn. China Machine Press, China (2010)","edition":"4"},{"key":"831_CR36","doi-asserted-by":"crossref","unstructured":"Schoenberg, I.J.: Contributions to the problem of approximation of equidistant data by analytic functions. Q. Appl. Math. 4(1), 45\u201399, 112\u2013141 (1946)","DOI":"10.1090\/qam\/15914"},{"key":"831_CR37","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1016\/0021-9045(76)90021-6","volume":"18","author":"LL Schumaker","year":"1976","unstructured":"Schumaker, L.L.: On Tchebycheffian spline functions. J. Approx. Theory 18, 278\u2013303 (1976)","journal-title":"J. Approx. Theory"},{"key":"831_CR38","volume-title":"Spline Functions: Basic Theory","author":"LL Schumaker","year":"1981","unstructured":"Schumaker, L.L.: Spline Functions: Basic Theory. Wiley, New York (1981)"},{"key":"831_CR39","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/0021-9045(82)90067-3","volume":"36","author":"LL Schumaker","year":"1982","unstructured":"Schumaker, L.L.: On recursions for generalized splines. J. Approx. Theory 36, 16\u201331 (1982)","journal-title":"J. Approx. Theory"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-016-0831-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-016-0831-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-016-0831-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-016-0831-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,24]],"date-time":"2017-06-24T19:34:13Z","timestamp":1498332853000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-016-0831-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,30]]},"references-count":39,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,4]]}},"alternative-id":["831"],"URL":"https:\/\/doi.org\/10.1007\/s00211-016-0831-0","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,7,30]]}}}