Approximation by hyperbolic splines
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXI, Tome 472 (2018), pp. 179-194 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper considers the minimal hyperbolic splines and their properties. Formulas for constructing quadratic splines and the corresponding biorthogonal (dual) functionals are obtained. Numerical results, demonstrating how approximation quality can be improved by using hyperbolic splines and changing control parameters, are presented.
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E. K. Kulikov; A. A. Makarov. Approximation by hyperbolic splines. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXI, Tome 472 (2018), pp. 179-194. http://geodesic.mathdoc.fr/item/ZNSL_2018_472_a12/

[1] D. G. Schweikert, “An interpolating curve using a spline in tension”, J. Math. Phys., 45 (1966), 312–317 | DOI | MR | Zbl

[2] H. Späth, “Exponential spline interpolation”, Computing, 4 (1969), 225–233 | DOI | MR | Zbl

[3] J. W. Jerome, L. L. Schumaker, “Local support bases for a class of spline functions”, J. Approx. Theory, 16 (1976), 16–27 | DOI | MR | Zbl

[4] C. de Boor, A Practical Guide to Splines, Revised edn., Springer, New York, 2001 | MR | Zbl

[5] L. L. Schumaker, Spline Functions: Basic Theory, 3rd edn., Cambridge University Press, Cambridge, 2007 | MR | Zbl

[6] B. I. Kvasov, P. Sattayatham, “$GB$-splines of arbitrary order”, J. Comput. Appl. Math., 104 (1999), 63–88 | DOI | MR | Zbl

[7] P. Costantini, T. Lyche, C. Manni, “On a class of weak Tchebycheff systems”, Numer. Math., 101 (2005), 333–354 | DOI | MR | Zbl

[8] Yu. K. Demyanovich, “Vlozhennye prostranstva trigonometricheskikh splainov i ikh vspleskovoe razlozhenie”, Mat. zametki, 78:5 (2005), 658–675 | DOI

[9] Yu. K. Demyanovich, “Gladkost prostranstv splainov i vspleskovye razlozheniya”, Dokl. RAN, 401:4 (2005), 1–4

[10] Yu. K. Demyanovich, “Minimalnye splainy lagranzheva tipa”, Probl. mat. analiza, 50 (2010), 21–64 | Zbl

[11] A. A. Makarov, “Normalizovannye trigonometricheskie splainy lagranzheva tipa”, Vestn. S.-Peterb. un-ta, 1:3 (2008), 81–87

[12] A. A. Makarov, “O postroenii splainov maksimalnoi gladkosti”, Probl. mat. analiza, 60 (2011), 25–38 | Zbl

[13] J. M. Pena, “Shape preserving representations for trigonometric polynomial curves”, Computer Aided Geometric Design, 14:1 (1997), 5–11 | DOI | MR | Zbl

[14] G. Xu, G. Z. Wang, “AHT Bezier curves and NUAHT B-spline curves”, J. Comp. Sci. Technol., 22:4 (2007), 597–607 | DOI | MR

[15] J. A. Cottrell, Th. J. R. Hughes, Yu. Bazilevs, Isogeometric Analysis: Towards Integration of CAD and FEA, John Wiley Sons, 2009 | MR

[16] B. I. Kvasov, Metody izogeometricheskoi approksimatsii splainami, Fizmatlit, M., 2006

[17] O. Kosogorov, A. Makarov, “On some piecewise quadratic spline functions”, Lect. Notes Comp. Sci., 10187, 2017, 448–455 | DOI | MR | Zbl

[18] Yu. K. Demyanovich, A. A. Makarov, “Neobkhodimye i dostatochnye usloviya neotritsatelnosti koordinatnykh trigonometricheskikh splainov vtorogo poryadka”, Vestn. S.-Peterb. un-ta. Ser. 1, 4 (62):1 (2017), 9–16

[19] A. A. Makarov, “O dvoistvennykh funktsionalakh k minimalnym splainam”, Zap. nauchn. semin. POMI, 453, 2016, 198–218

[20] A. A. Makarov, “Biortogonalnye sistemy funktsionalov i matritsy dekompozitsii dlya minimalnykh splainov”, Ukr. mat. visn., 9:2 (2012), 219–236 | Zbl

[21] Yu. S. Zavyalov, B. I. Kvasov, V. L. Miroshnichenko, Metody splain-funktsii, Nauka, M., 1980