{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T05:40:10Z","timestamp":1750830010214,"version":"3.41.0"},"publisher-location":"Cham","reference-count":35,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319663197"},{"type":"electronic","value":"9783319663203"}],"license":[{"start":{"date-parts":[[2017,1,1]],"date-time":"2017-01-01T00:00:00Z","timestamp":1483228800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017]]},"DOI":"10.1007\/978-3-319-66320-3_19","type":"book-chapter","created":{"date-parts":[[2017,8,29]],"date-time":"2017-08-29T11:34:27Z","timestamp":1504006467000},"page":"257-271","source":"Crossref","is-referenced-by-count":4,"title":["Non-linearity and Non-convexity in Optimal Knots Selection for Sparse Reduced Data"],"prefix":"10.1007","author":[{"given":"Ryszard","family":"Kozera","sequence":"first","affiliation":[]},{"given":"Lyle","family":"Noakes","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2017,8,30]]},"reference":[{"key":"19_CR1","volume-title":"Numerical Control: Mathematics and Applications","author":"PE B\u00e9zier","year":"1972","unstructured":"B\u00e9zier, P.E.: Numerical Control: Mathematics and Applications. Wiley, New York (1972)"},{"issue":"1","key":"19_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0167-8396(84)90003-7","volume":"1","author":"E Boehm","year":"1988","unstructured":"Boehm, E., Farin, G., Kahmann, J.: A survey of curve and surface methods in CAGD. Comput. Aided Geom. Des. 1(1), 1\u201360 (1988)","journal-title":"Comput. Aided Geom. Des."},{"key":"19_CR3","volume-title":"A Practical Guide to Spline","author":"C Boor de","year":"1985","unstructured":"de Boor, C.: A Practical Guide to Spline. Springer, New York (1985)"},{"key":"19_CR4","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"S Boyd","year":"2004","unstructured":"Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)"},{"key":"19_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"88","DOI":"10.1007\/978-3-642-23568-9_8","volume-title":"Computer Algebra in Scientific Computing","author":"DA Budzko","year":"2011","unstructured":"Budzko, D.A., Prokopenya, A.N.: On the stability of equilibrium positions in the circular restricted four-body problem. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2011. LNCS, vol. 6885, pp. 88\u2013100. Springer, Heidelberg (2011). doi: 10.1007\/978-3-642-23568-9_8"},{"key":"19_CR6","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1137\/0713025","volume":"13","author":"MP Epstein","year":"1976","unstructured":"Epstein, M.P.: On the influence of parameterization in parametric interpolation. SIAM J. Numer. Anal. 13, 261\u2013268 (1976)","journal-title":"SIAM J. Numer. Anal."},{"key":"19_CR7","volume-title":"Curves and Surfaces for Computer Aided Geometric Design","author":"G Farin","year":"1993","unstructured":"Farin, G.: Curves and Surfaces for Computer Aided Geometric Design. Academic Press, San Diego (1993)"},{"issue":"2","key":"19_CR8","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/S0167-8396(96)00026-X","volume":"14","author":"RT Farouki","year":"1997","unstructured":"Farouki, R.T.: Optimal parameterizations. Comput. Aided Geom. Des. 14(2), 153\u2013168 (1997)","journal-title":"Comput. Aided Geom. Des."},{"key":"19_CR9","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1093\/imanum\/dri022","volume":"26","author":"MS Floater","year":"2006","unstructured":"Floater, M.S.: Chordal cubic spline interpolation is fourth order accurate. IMA J. Numer. Anal. 26, 25\u201333 (2006)","journal-title":"IMA J. Numer. Anal."},{"issue":"1","key":"19_CR10","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/0167-8396(88)90017-9","volume":"5","author":"J Hoschek","year":"1988","unstructured":"Hoschek, J.: Intrinsic parametrization for approximation. Comput. Aided Geom. Des. 5(1), 27\u201331 (1988)","journal-title":"Comput. Aided Geom. Des."},{"issue":"18","key":"19_CR11","doi-asserted-by":"crossref","first-page":"28","DOI":"10.5604\/20804075.1049599","volume":"7","author":"M Janik","year":"2013","unstructured":"Janik, M., Kozera, R., Kozio\u0142, P.: Reduced data for curve modeling - applications in graphics, computer vision and physics. Adv. Sci. Tech. 7(18), 28\u201335 (2013)","journal-title":"Adv. Sci. Tech."},{"key":"19_CR12","first-page":"95","volume":"5","author":"LM Koci\u0107","year":"1990","unstructured":"Koci\u0107, L.M., Simoncinelli, A.C., Della, V.B.: Blending parameterization of polynomial and spline interpolants. Facta Universitatis (NI\u0160), Ser. Math. Inform. 5, 95\u2013107 (1990)","journal-title":"Facta Universitatis (NI\u0160), Ser. Math. Inform."},{"key":"19_CR13","first-page":"1","volume":"25","author":"R Kozera","year":"2004","unstructured":"Kozera, R.: Curve modelling via interpolation based on multidimensional reduced data. Stud. Informatica 25, 1\u2013140 (2004). (4B(61))","journal-title":"Stud. Informatica"},{"key":"19_CR14","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1016\/j.amc.2013.06.060","volume":"221","author":"R Kozera","year":"2013","unstructured":"Kozera, R., Noakes, L.: Piecewise-quadratics and exponential parameterizations for reduced data. Appl. Maths Comput. 221, 620\u2013638 (2013)","journal-title":"Appl. Maths Comput."},{"issue":"3\u20134","key":"19_CR15","doi-asserted-by":"crossref","first-page":"285","DOI":"10.3233\/FUN-2004-613-406","volume":"61","author":"R Kozera","year":"2004","unstructured":"Kozera, R., Noakes, L.: $$C^1$$ Interpolation with cumulative chord cubics. Fundamenta Informaticae 61(3\u20134), 285\u2013301 (2004)","journal-title":"Fundamenta Informaticae"},{"key":"19_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"613","DOI":"10.1007\/3-540-47967-8_41","volume-title":"Computer Vision \u2014 ECCV 2002","author":"L Noakes","year":"2002","unstructured":"Noakes, L., Kozera, R.: Interpolating sporadic data. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2351, pp. 613\u2013625. Springer, Heidelberg (2002). doi: 10.1007\/3-540-47967-8_41"},{"key":"19_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-319-30285-0_1","volume-title":"Image and Video Technology \u2013 PSIVT 2015 Workshops","author":"R Kozera","year":"2016","unstructured":"Kozera, R., Noakes, L.: Optimal knots selection for sparse reduced data. In: Huang, F., Sugimoto, A. (eds.) PSIVT 2015. LNCS, vol. 9555, pp. 3\u201314. Springer, Cham (2016). doi: 10.1007\/978-3-319-30285-0_1"},{"key":"19_CR18","series-title":"SPIE 2016","volume-title":"Photonics, Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2016","author":"R Kozera","year":"2016","unstructured":"Kozera, R., Noakes, L.: Modeling reduced sparse data. In: Romaniuk, R.S. (ed.) Photonics, Applications in Astronomy, Communications, Industry, and High-Energy Physics Experiments 2016. SPIE 2016, vol. 10031. Society of Photo-Optical Instrumentation Engineers, Bellingham (2016)"},{"key":"19_CR19","unstructured":"Kozera, R., Noakes, L.: Fitting Data via Optimal Interpolation Knots. (Submitted)"},{"key":"19_CR20","doi-asserted-by":"crossref","DOI":"10.1142\/4172","volume-title":"Methods of Shape-Preserving Spline Approximation","author":"BI Kvasov","year":"2000","unstructured":"Kvasov, B.I.: Methods of Shape-Preserving Spline Approximation. World Scientific, Singapore (2000)"},{"key":"19_CR21","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/j.cam.2005.06.040","volume":"191","author":"EB Kuznetsov","year":"2006","unstructured":"Kuznetsov, E.B., Yakimovich, A.Y.: The best parameterization for parametric interpolation. J. Comp. Appl. Maths 191, 239\u2013245 (2006)","journal-title":"J. Comp. Appl. Maths"},{"key":"19_CR22","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/0021-9045(84)90121-7","volume":"41","author":"SP Marin","year":"1984","unstructured":"Marin, S.P.: An approach to data parameterization in parametric cubic spline interpolation problems. J. Approx. Theory 41, 64\u201386 (1984)","journal-title":"J. Approx. Theory"},{"issue":"217","key":"19_CR23","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1090\/S0025-5718-97-00796-5","volume":"66","author":"K M\u00f8rken","year":"1997","unstructured":"M\u00f8rken, K., Scherer, K.: A general framework for high-accuracy parametric interpolation. Math. Comput. 66(217), 237\u2013260 (1997)","journal-title":"Math. Comput."},{"key":"19_CR24","first-page":"37","volume":"64","author":"L Noakes","year":"1999","unstructured":"Noakes, L.: A global algorithm for geodesics. J. Math. Austral. Soc. Ser. A 64, 37\u201350 (1999)","journal-title":"J. Math. Austral. Soc. Ser. A"},{"key":"19_CR25","series-title":"Computational Imaging and Vision","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/1-4020-3858-8_4","volume-title":"Geometric Properties from Incomplete Data","author":"L Noakes","year":"2006","unstructured":"Noakes, L., Kozera, R.: Cumulative chords piecewise-quadratics and piecewise-cubics. In: Klette, R., Kozera, R., Noakes, L., Weickert, J. (eds.) Geometric Properties from Incomplete Data. Computational Imaging and Vision, vol. 31, pp. 59\u201375. Springer, The Netherlands (2006)"},{"issue":"3","key":"19_CR26","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1090\/qam\/1999832","volume":"61","author":"L Noakes","year":"2003","unstructured":"Noakes, L., Kozera, R.: More-or-less uniform sampling and lengths of curves. Quar. Appl. Maths 61(3), 475\u2013484 (2003)","journal-title":"Quar. Appl. Maths"},{"issue":"3","key":"19_CR27","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1023\/A:1022104332058","volume":"18","author":"L Noakes","year":"2003","unstructured":"Noakes, L., Kozera, R.: Nonlinearities and noise reduction in 3-source photometric stereo. J. Math. Imag. Vis. 18(3), 119\u2013127 (2003)","journal-title":"J. Math. Imag. Vis."},{"key":"19_CR28","series-title":"Vision Geometry VIII","first-page":"317","volume-title":"SPIE 1999","author":"L Noakes","year":"1999","unstructured":"Noakes, L., Kozera, R.: 2D leap-frog algorithm for optimal surface reconstruction. In: Latecki, M.J. (ed.) SPIE 1999. Vision Geometry VIII, vol. 3811, pp. 317\u2013328. Society of Industrial and Applied Mathematics, Bellingham (1999)"},{"key":"19_CR29","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1137\/0729035","volume":"29","author":"ETY Lee","year":"1992","unstructured":"Lee, E.T.Y.: Corners, cusps, and parameterization: variations on a theorem of Epstein. SIAM J. Numer. Anal. 29, 553\u2013565 (1992)","journal-title":"SIAM J. Numer. Anal."},{"key":"19_CR30","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/0010-4485(89)90003-1","volume":"21","author":"ETY Lee","year":"1989","unstructured":"Lee, E.T.Y.: Choosing nodes in parametric curve interpolation. Comput. Aided Geom. Des. 21, 363\u2013370 (1989)","journal-title":"Comput. Aided Geom. Des."},{"key":"19_CR31","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-59223-2","volume-title":"The NURBS Book","author":"L Piegl","year":"1997","unstructured":"Piegl, L., Tiller, W.: The NURBS Book. Springer, Berlin (1997)"},{"issue":"3","key":"19_CR32","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1134\/S0361768812030048","volume":"38","author":"AN Prokopenya","year":"2012","unstructured":"Prokopenya, A.N.: Hamiltonian normalization in the restricted many-body problem by computer algebra methods. Program. Comput. Softw. 38(3), 156\u2013166 (2012)","journal-title":"Program. Comput. Softw."},{"key":"19_CR33","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/0167-8396(94)00004-C","volume":"12","author":"A Rababah","year":"1995","unstructured":"Rababah, A.: High order approximation methods for curves. Comput. Aided Geom. Des. 12, 89\u2013102 (1995)","journal-title":"Comput. Aided Geom. Des."},{"key":"19_CR34","first-page":"1","volume-title":"Mathematical Methods for Curves and Surfaces II","author":"R Schaback","year":"1998","unstructured":"Schaback, R.: Optimal geometric Hermite interpolation of curves. In: D\u00e6hlen, M., Lyche, T., Schumaker, L. (eds.) Mathematical Methods for Curves and Surfaces II, pp. 1\u201312. Vanderbilt University Press, Nashville (1998)"},{"key":"19_CR35","volume-title":"The Mathematica Book","author":"S Wolfram","year":"2003","unstructured":"Wolfram, S.: The Mathematica Book, 5th edn. Wolfram Media, Champaign (2003)","edition":"5"}],"container-title":["Lecture Notes in Computer Science","Computer Algebra in Scientific Computing"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-66320-3_19","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T05:10:40Z","timestamp":1750828240000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-66320-3_19"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017]]},"ISBN":["9783319663197","9783319663203"],"references-count":35,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-66320-3_19","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2017]]}}}