Approximation of Set-Valued Functions with images sets in ℝd.

Nira Dyn Tel Aviv University, School of Mathematical Sciences, Israel https://zbmath.org/authors/?q=ai:dyn.nira https://mathscinet.ams.org/mathscinet/MRAuthorID/61245 https://mathgenealogy.org/id.php?id=19294 https://en.wikipedia.org/wiki/Nira_Dyn https://www.wikidata.org/entity/Q56087039 https://id.loc.gov/authorities/names/no97066815 https://d-nb.info/gnd/1065934696

Nira Dyn David Levin Approximation of Set-Valued Functions with images sets in ℝd. 2025 January abs/2501.14591 CoRR https://doi.org/10.48550/arXiv.2501.14591 db/journals/corr/corr2501.html#abs-2501-14591 streams/journals/corr

Nira Dyn Nir Sharon Subdivision Schemes in Metric Spaces. 2025 September abs/2509.08070 CoRR https://doi.org/10.48550/arXiv.2509.08070 db/journals/corr/corr2509.html#abs-2509-08070 streams/journals/corr

Hofit Ben-Zion Vardi Nira Dyn Nir Sharon Hermite subdivision schemes for manifold-valued Hermite data. 102342 2024 111 Comput. Aided Geom. Des. https://doi.org/10.1016/j.cagd.2024.102342 db/journals/cagd/cagd111.html#VardiDS24

Nira Dyn Nir Sharon Improving the convergence analysis of linear subdivision schemes. 2024 abs/2405.09414 CoRR https://doi.org/10.48550/arXiv.2405.09414 db/journals/corr/corr2405.html#abs-2405-09414

Hofit Ben-Zion Vardi Nira Dyn Nir Sharon Geometric Hermite interpolation in $\mathbb {R}^{n}$ by refinements. 38 2023 49 Adv. Comput. Math. 3 https://doi.org/10.1007/s10444-023-10037-z db/journals/adcm/adcm49.html#VardiDS23

Nira Dyn Kai Hormann Claudio Mancinelli Non-uniform interpolatory subdivision schemes with improved smoothness. 102083 2022 94 Comput. Aided Geom. Des. https://doi.org/10.1016/j.cagd.2022.102083 db/journals/cagd/cagd94.html#DynHM22

Hofit Ben-Zion Vardi Nira Dyn Nir Sharon Geometric Hermite Interpolation in Rn by Refinements. 2022 abs/2203.02903 CoRR https://doi.org/10.48550/arXiv.2203.02903 db/journals/corr/corr2203.html#abs-2203-02903

Qusay Muzaffar Nira Dyn David Levin Interpolation of Set-Valued Functions. 2022 abs/2208.14929 CoRR https://doi.org/10.48550/arXiv.2208.14929 db/journals/corr/corr2208.html#abs-2208-14929

Maria Charina Costanza Conti Nira Dyn Multivariate compactly supported C∞ functions by subdivision. 2022 abs/2211.05677 CoRR https://doi.org/10.48550/arXiv.2211.05677 db/journals/corr/corr2211.html#abs-2211-05677

Elena E. Berdysheva Nira Dyn Elza M. Farkhi Alona Mokhov Metric approximation of set-valued functions of bounded variation by integral operators. 2022 abs/2212.00439 CoRR https://doi.org/10.48550/arXiv.2212.00439 db/journals/corr/corr2212.html#abs-2212-00439

Evgeny Lipovetsky Nira Dyn Extending Editing Capabilities of Subdivision Schemes by Refinement of Point-Normal Pairs. 102865 2020 126 Comput. Aided Des. https://doi.org/10.1016/j.cad.2020.102865 db/journals/cad/cad126.html#LipovetskyD20

Nira Dyn Bert Jüttler Dominik Mokris On the error in transfinite interpolation by low-rank functions. 105379 2020 253 J. Approx. Theory https://doi.org/10.1016/j.jat.2020.105379 db/journals/jat/jat253.html#DynJM20

Nira Dyn Elza M. Farkhi Shirley Keinan Approximation of 3D objects by piecewise linear geometric interpolants of their 1D cross-sections. 2020 368 J. Comput. Appl. Math. https://doi.org/10.1016/j.cam.2019.112466 db/journals/jcam/jcam368.html#DynFK20

Costanza Conti Nira Dyn Lucia Romani Convergence analysis of corner cutting algorithms refining nets of functions. 134-146 2020 176 Math. Comput. Simul. https://doi.org/10.1016/j.matcom.2020.01.012 db/journals/mcs/mcs176.html#ContiDR20

Elena E. Berdysheva Nira Dyn Elza M. Farkhi Alona Mokhov Metric Fourier approximation of set-valued functions of bounded variation. 2020 abs/2008.10340 CoRR https://arxiv.org/abs/2008.10340 db/journals/corr/corr2008.html#abs-2008-10340

Evgeny Lipovetsky Nira Dyn C1 analysis of some 2D subdivision schemes refining point-normal pairs with the circle average. 45-54 2019 69 Comput. Aided Geom. Des. https://doi.org/10.1016/j.cagd.2019.01.001 https://www.wikidata.org/entity/Q128519673 db/journals/cagd/cagd69.html#LipovetskyD19

Nira Dyn Ron Goldman 0002 David Levin High order smoothness of non-linear Lane-Riesenfeld algorithms in the functional setting. 119-129 2019 71 Comput. Aided Geom. Des. https://doi.org/10.1016/j.cagd.2019.03.003 https://www.wikidata.org/entity/Q128060068 db/journals/cagd/cagd71.html#DynGL19

Elena E. Berdysheva Nira Dyn Elza M. Farkhi Alona Mokhov Metric approximation of set-valued functions of bounded variation. 251-264 2019 349 J. Comput. Appl. Math. https://doi.org/10.1016/j.cam.2018.09.039 https://www.wikidata.org/entity/Q129152588 db/journals/jcam/jcam349.html#BerdyshevaDFM19

Maria Charina Nira Dyn Vladimir Yu. Protasov Analytic functions in shift-invariant spaces and analytic limits of level dependent subdivision. 2019 abs/1907.05658 CoRR http://arxiv.org/abs/1907.05658 db/journals/corr/corr1907.html#abs-1907-05658

Evgeny Lipovetsky Nira Dyn Extending editing capabilities of subdivision schemes by refinement of point-normal pairs. 2019 abs/1908.06154 CoRR http://arxiv.org/abs/1908.06154 db/journals/corr/corr1908.html#abs-1908-06154

Costanza Conti Nira Dyn Convergence and smoothness of tensor-product of two non-uniform linear subdivision schemes. 16-18 2018 66 Comput. Aided Geom. Des. https://doi.org/10.1016/j.cagd.2018.08.001 https://www.wikidata.org/entity/Q129388464 db/journals/cagd/cagd66.html#ContiD18

Nira Dyn Nir Sharon Manifold-valued subdivision schemes based on geodesic inductive averaging. 54-67 2017 311 J. Comput. Appl. Math. https://doi.org/10.1016/j.cam.2016.07.008 db/journals/jcam/jcam311.html#DynS17

Nira Dyn Nir Sharon A global approach to the refinement of manifold data. 2017 86 Math. Comput. 303 https://doi.org/10.1090/mcom/3087 db/journals/moc/moc86.html#DynS17 375-395

Evgeny Lipovetsky Nira Dyn A weighted binary average of point-normal pairs with application to subdivision schemes. 36-48 2016 48 Comput. Aided Geom. Des. https://doi.org/10.1016/j.cagd.2016.07.004 db/journals/cagd/cagd48.html#LipovetskyD16

Evgeny Lipovetsky Nira Dyn A weighted binary average of point-normal pairs with application to subdivision schemes. 2016 abs/1608.04082 CoRR http://arxiv.org/abs/1608.04082 db/journals/corr/corr1608.html#LipovetskyD16

Costanza Conti Nira Dyn Carla Manni Marie-Laurence Mazure Convergence of univariate non-stationary subdivision schemes via asymptotic similarity. 1-8 2015 37 Comput. Aided Geom. Des. https://doi.org/10.1016/j.cagd.2015.06.004 db/journals/cagd/cagd37.html#ContiDMM15

Nira Dyn Allison Heard Kai Hormann Nir Sharon Univariate subdivision schemes for noisy data with geometric applications. 85-104 2015 37 Comput. Aided Geom. Des. https://doi.org/10.1016/j.cagd.2015.06.003 db/journals/cagd/cagd37.html#DynHHS15

Nira Dyn Pavel Kozlov Adaptive thinning of centers for approximation of a large data set by radial functions. 153-169 2015 200 J. Approx. Theory https://doi.org/10.1016/j.jat.2015.07.005 db/journals/jat/jat200.html#DynK15

Nira Dyn Elza M. Farkhi Alona Mokhov Approximation of Set-Valued Functions - Adaptation of Classical Approximation Operator. 1-153 Imperial College Press 2014 978-1-78326-302-8

Nira Dyn Michael S. Floater Multivariate polynomial interpolation on lower sets. 34-42 2014 177 J. Approx. Theory https://doi.org/10.1016/j.jat.2013.09.008 db/journals/jat/jat177.html#DynF14

Nira Dyn Maria Skopina Decompositions of trigonometric polynomials with applications to multivariate subdivision schemes. 321-349 2013 38 Adv. Comput. Math. 2 https://doi.org/10.1007/s10444-011-9239-7 db/journals/adcm/adcm38.html#DynS13

Shay Kels Nira Dyn Subdivision Schemes of Sets and the Approximation of Set-Valued Functions in the Symmetric Difference Metric. 835-865 2013 13 Found. Comput. Math. 5 https://doi.org/10.1007/s10208-013-9146-z db/journals/focm/focm13.html#KelsD13

Nira Dyn Kai Hormann Geometric conditions for tangent continuity of interpolatory planar subdivision curves. 332-347 2012 29 Comput. Aided Geom. Des. 6 https://doi.org/10.1016/j.cagd.2012.02.004 db/journals/cagd/cagd29.html#DynH12

Costanza Conti Nira Dyn Lucia Romani Interpolatory blending net subdivision schemes of Dubuc-Deslauriers type. 722-735 2012 29 Comput. Aided Geom. Des. 9 https://doi.org/10.1016/j.cagd.2012.08.001 db/journals/cagd/cagd29.html#ContiDR12

Nir Sharon Nira Dyn Bivariate interpolation based on univariate subdivision schemes. 709-730 2012 164 J. Approx. Theory 5 https://doi.org/10.1016/j.jat.2012.02.002 db/journals/jat/jat164.html#SharonD12

Albert Cohen 0002 Nira Dyn Frédéric Hecht Jean-Marie Mirebeau Adaptive multiresolution analysis based on anisotropic triangulations. 2012 81 Math. Comput. 278 https://doi.org/10.1090/S0025-5718-2011-02495-6 db/journals/moc/moc81.html#CohenDHM12 789-810

Shay Kels Nira Dyn Reconstruction of 3D objects from 2D cross-sections with the 4-point subdivision scheme adapted to sets. 741-746 2011 35 Comput. Graph. 3 https://doi.org/10.1016/j.cag.2011.03.007 db/journals/cg/cg35.html#KelsD11

Nira Dyn Ron Goldman 0002 Convergence and Smoothness of Nonlinear Lane-Riesenfeld Algorithms in the Functional Setting. 79-94 2011 11 Found. Comput. Math. 1 https://doi.org/10.1007/s10208-010-9080-2 db/journals/focm/focm11.html#DynG11

Costanza Conti Nira Dyn Analysis of subdivision schemes for nets of functions by proximity and controllability. 461-475 2011 236 J. Comput. Appl. Math. 4 https://doi.org/10.1016/j.cam.2011.06.004 db/journals/jcam/jcam236.html#ContiD11

Mira Bozzini Nira Dyn Milvia Rossini Construction of generators of quasi-interpolation operators of high approximation orders in spaces of polyharmonic splines. 557-564 2011 236 J. Comput. Appl. Math. 4 https://doi.org/10.1016/j.cam.2011.07.002 db/journals/jcam/jcam236.html#BozziniDR11

Shay Kels Nira Dyn Evgeny Lipovetsky Computation of the Metric Average of 2D Sets with Piecewise Linear Boundaries. 265-275 2010 3 Algorithms 3 https://doi.org/10.3390/a3030265 db/journals/algorithms/algorithms3.html#KelsDL10

Costanza Conti Nira Dyn Blending based corner cutting subdivision scheme for nets of curves. 340-358 2010 27 Comput. Aided Geom. Des. 4 https://doi.org/10.1016/j.cagd.2009.12.006 db/journals/cagd/cagd27.html#ContiD10

Nira Dyn Philipp Grohs Johannes Wallner 0001 Approximation order of interpolatory nonlinear subdivision schemes. 1697-1703 2010 233 J. Comput. Appl. Math. 7 https://doi.org/10.1016/j.cam.2009.02.017 db/journals/jcam/jcam233.html#DynGW10

Nira Dyn Michael S. Floater Kai Hormann Four-point curve subdivision based on iterated chordal and centripetal parameterizations. 279-286 2009 26 Comput. Aided Geom. Des. 3 https://doi.org/10.1016/j.cagd.2008.09.006 db/journals/cagd/cagd26.html#DynFH09

Nira Dyn Elza M. Farkhi Alona Mokhov Multi-segmental representations and approximation of set-valued functions with 1D images. 39-60 2009 159 J. Approx. Theory 1 https://doi.org/10.1016/j.jat.2008.11.013 db/journals/jat/jat159.html#DynFM09

Ziv Ayalon Nira Dyn David Levin Piecewise L-splines of order 4: Interpolation and L2 error bounds for splines in tension. 421-431 2009 161 J. Approx. Theory 2 https://doi.org/10.1016/j.jat.2008.10.008 db/journals/jat/jat161.html#AyalonDL09

Tamir Tassa Nira Dyn Multipartite Secret Sharing by Bivariate Interpolation. 227-258 2009 22 J. Cryptol. 2 https://doi.org/10.1007/s00145-008-9027-9 db/journals/joc/joc22.html#TassaD09

Nira Dyn Armin Iske Holger Wendland Meshfree Thinning of 3D Point Clouds. 409-425 2008 8 Found. Comput. Math. 4 https://doi.org/10.1007/s10208-007-9008-7 db/journals/focm/focm8.html#DynIW08

Nira Dyn Kai Hormann Malcolm A. Sabin Zuowei Shen Polynomial reproduction by symmetric subdivision schemes. 28-42 2008 155 J. Approx. Theory 1 https://doi.org/10.1016/j.jat.2008.04.008 db/journals/jat/jat155.html#DynHSS08

Evgeny Lipovetsky Nira Dyn An efficient algorithm for the computation of the metric average of two intersecting convex polygons, with application to morphing. 269-282 2007 26 Adv. Comput. Math. 1-3 https://doi.org/10.1007/s10444-005-7473-6 db/journals/adcm/adcm26.html#LipovetskyD07

Carsten Moenning Facundo Mémoli Guillermo Sapiro Nira Dyn Neil A. Dodgson Meshless geometric subdivision. 160-179 2007 69 Graph. Model. 3-4 https://doi.org/10.1016/j.gmod.2006.11.001 https://www.wikidata.org/entity/Q59751313 db/journals/cvgip/cvgip69.html#MoenningMSDD07

Nira Dyn David Levin Jungho Yoon Analysis of Univariate Nonstationary Subdivision Schemes with Application to Gaussian-Based Interpolatory Schemes. 470-488 2007 39 SIAM J. Math. Anal. 2 https://doi.org/10.1137/050638217 db/journals/siamma/siamma39.html#DynLY07

Roman Kazinnik Shai Dekel Nira Dyn Low Bit-Rate Image Coding Using Adaptive Geometric Piecewise Polynomial Approximation. 2225-2233 2007 16 IEEE Trans. Image Process. 9 https://doi.org/10.1109/TIP.2007.903250 https://www.wikidata.org/entity/Q51906704 db/journals/tip/tip16.html#KazinnikDD07

Laurent Demaret Nira Dyn Armin Iske Image compression by linear splines over adaptive triangulations. 1604-1616 2006 86 Signal Process. 7 https://doi.org/10.1016/j.sigpro.2005.09.003 db/journals/sigpro/sigpro86.html#DemaretDI06

Tamir Tassa Nira Dyn Multipartite Secret Sharing by Bivariate Interpolation. 288-299 2006 conf/icalp/2006-2 ICALP (2) https://doi.org/10.1007/11787006_25 db/conf/icalp/icalp2006-2.html#TassaD06

Johannes Wallner 0001 Nira Dyn Convergence and C1 analysis of subdivision schemes on manifolds by proximity. 593-622 2005 22 Comput. Aided Geom. Des. 7 https://doi.org/10.1016/j.cagd.2005.06.003 db/journals/cagd/cagd22.html#WallnerD05

Francesc Aràndiga Albert Cohen 0002 Rosa Donat Nira Dyn Interpolation and Approximation of Piecewise Smooth Functions. 41-57 2005 43 SIAM J. Numer. Anal. 1 https://doi.org/10.1137/S0036142903426245 db/journals/siamnum/siamnum43.html#ArandigaCDD05

Nurit Alkalai Nira Dyn Optimising 3D Triangulations: Improving the Initial Triangulation for the Butterfly Subdivision Scheme. 231-244 2005 Advances in Multiresolution for Geometric Modelling https://doi.org/10.1007/3-540-26808-1_12 books/sp/DFS2005 db/books/collections/DFS2005.html#AlkalaiD05 Martin Marinov Nira Dyn David Levin Geometrically Controlled 4-Point Interpolatory Schemes. 301-315 2005 Advances in Multiresolution for Geometric Modelling https://doi.org/10.1007/3-540-26808-1_17 books/sp/DFS2005 db/books/collections/DFS2005.html#MarinovDL05 Laurent Demaret Nira Dyn Michael S. Floater Armin Iske Adaptive Thinning for Terrain Modelling and Image Compression. 319-338 2005 Advances in Multiresolution for Geometric Modelling https://doi.org/10.1007/3-540-26808-1_18 books/sp/DFS2005 db/books/collections/DFS2005.html#DemaretDFI05

Alla Sheffer Craig Gotsman Nira Dyn Robust Spherical Parameterization of Triangular Meshes. 185-193 2004 72 Computing 1-2 https://doi.org/10.1007/s00607-004-0056-9 db/journals/computing/computing72.html#ShefferGD04

Nira Dyn David Levin Ariel Luzzatto Exponentials Reproducing Subdivision Schemes. 187-206 2003 3 Found. Comput. Math. 2 https://doi.org/10.1007/s10208-001-0047-1 db/journals/focm/focm3.html#DynLL03

Nira Dyn Interpolatory Subdivision Schemes. 25-50 2002 Tutorials on Multiresolution in Geometric Modelling https://doi.org/10.1007/978-3-662-04388-2_2 books/sp/IQF2002 db/books/collections/IQF2002.html#Dyn02 Nira Dyn Analysis of Convergence and Smoothness by the Formalism of Laurent Polynomials. 51-68 2002 Tutorials on Multiresolution in Geometric Modelling https://doi.org/10.1007/978-3-662-04388-2_3 books/sp/IQF2002 db/books/collections/IQF2002.html#Dyn02a

Nira Dyn Frans Kuijt David Levin Ruud van Damme Convexity preservation of the four-point interpolatory subdivision scheme. 789-792 1999 16 Comput. Aided Geom. Des. 8 https://doi.org/10.1016/S0167-8396(99)00019-9 db/journals/cagd/cagd16.html#DynKLD99

Nur Arad Nira Dyn Daniel Reisfeld Yehezkel Yeshurun Image Warping by Radial Basis Functions: Application to Facial Expressions. 161-172 1994 56 CVGIP Graph. Model. Image Process. 2 db/journals/cvgip/cvgip56.html#AradDRY94 https://doi.org/10.1006/cgip.1994.1015

Nira Dyn The Work of John Gregory, Rational Spline Interpolation, Subdivision Algorithms and C Polygonal Patches. 21-41 1994 conf/ima-ms/1994 IMA Conference on the Mathematics of Surfaces db/conf/ima-ms/ima-ms1994.html#Dyn94

Nira Dyn Ifat Goren Shmuel Rippa Transforming triangulations in polygonal domains. 531-536 1993 10 Comput. Aided Geom. Des. 6 https://doi.org/10.1016/0167-8396(93)90029-3 https://www.wikidata.org/entity/Q126582415 db/journals/cagd/cagd10.html#DynGR93

Nira Dyn David Levin Dingyuan Liu Interpolatory convexity-preserving subdivision schemes for curves and surfaces. 211-216 1992 24 Comput. Aided Des. 4 https://doi.org/10.1016/0010-4485(92)90057-H db/journals/cad/cad24.html#DynLL92

Martin D. Buhmann Nira Dyn Error Estimates for Multiquadric Interpolation. 51-58 1991 Curves and Surfaces https://doi.org/10.1016/b978-0-12-438660-0.50013-3 books/ap/91/LMS1991 db/books/collections/LMS1991.html#BuhmannD91 Nira Dyn David Levin I. Yad-Shalom Regularity Conditions for a Class of Geometrically Continuous Curves and Surfaces. 169-176 1991 Curves and Surfaces https://doi.org/10.1016/b978-0-12-438660-0.50029-7 books/ap/91/LMS1991 db/books/collections/LMS1991.html#DynLY91

Nira Dyn David Levin Charles A. Micchelli Using parameters to increase smoothness of curves and surfaces generated by subdivision. 129-140 1990 7 Comput. Aided Geom. Des. 1-4 https://doi.org/10.1016/0167-8396(90)90025-M db/journals/cagd/cagd7.html#DynLM90

Nira Dyn David Levine John A. Gregory A butterfly subdivision scheme for surface interpolation with tension control. 160-169 1990 9 ACM Trans. Graph. 2 https://doi.org/10.1145/78956.78958 db/journals/tog/tog9.html#DynLG90

Nira Dyn David Levin John A. Gregory A 4-point interpolatory subdivision scheme for curve design. 257-268 1987 4 Comput. Aided Geom. Des. 4 https://doi.org/10.1016/0167-8396(87)90001-X db/journals/cagd/cagd4.html#DynLG87

Nira Dyn Interpolation of scattered Data by radial Functions. 47-61 1987 Topics in Multivariate Approximation https://doi.org/10.1016/b978-0-12-174585-1.50009-9 books/ap/87/CSU1987 db/books/collections/CSU1987.html#Dyn87 Nurit Alkalai Nur Arad Francesc Aràndiga Ziv Ayalon Elena E. Berdysheva Mira Bozzini Martin D. Buhmann Maria Charina Albert Cohen 0002 Costanza Conti Ruud van Damme Shai Dekel Laurent Demaret Neil A. Dodgson Rosa Donat Elza M. Farkhi Michael S. Floater Ron Goldman 0002 Ifat Goren Craig Gotsman John A. Gregory Philipp Grohs Allison Heard Frédéric Hecht Kai Hormann Armin Iske Bert Jüttler Roman Kazinnik Shirley Keinan Shay Kels Pavel Kozlov Frans Kuijt David Levin David Levine Evgeny Lipovetsky Dingyuan Liu Ariel Luzzatto Claudio Mancinelli Carla Manni Martin Marinov Marie-Laurence Mazure Facundo Mémoli Charles A. Micchelli Jean-Marie Mirebeau Carsten Moenning Alona Mokhov Dominik Mokris Qusay Muzaffar Vladimir ProtasovVladimir Yu. Protasov Daniel Reisfeld Shmuel Rippa Lucia Romani Milvia Rossini Malcolm A. Sabin Guillermo Sapiro Nir Sharon Alla Sheffer Zuowei Shen Maria Skopina Tamir Tassa Hofit Ben-Zion Vardi Johannes Wallner 0001 Holger Wendland I. Yad-Shalom Yehezkel Yeshurun Jungho Yoon