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Journal articles on the topic 'Interpolation sets'

Author: Grafiati

Published: 28 May 2022

Last updated: 31 July 2025

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1

Le, Anh N. "Sublacunary sets and interpolation sets for nilsequences." Discrete & Continuous Dynamical Systems 42, no. 4 (2022): 1855. http://dx.doi.org/10.3934/dcds.2021175.

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<p style='text-indent:20px;'>A set <inline-formula><tex-math id="M1">\begin{document}$ E \subset \mathbb{N} $\end{document}</tex-math></inline-formula> is an interpolation set for nilsequences if every bounded function on <inline-formula><tex-math id="M2">\begin{document}$ E $\end{document}</tex-math></inline-formula> can be extended to a nilsequence on <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{N} $\end{document}</tex-math></inline-formula>. Following a theorem of Strzelecki, every lacunary set is a

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2

Feng, Renzhong, and Yanan Zhang. "Piecewise Bivariate Hermite Interpolations for Large Sets of Scattered Data." Journal of Applied Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/239703.

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The requirements for interpolation of scattered data are high accuracy and high efficiency. In this paper, a piecewise bivariate Hermite interpolant satisfying these requirements is proposed. We firstly construct a triangulation mesh using the given scattered point set. Based on this mesh, the computational point (x,y) is divided into two types: interior point and exterior point. The value of Hermite interpolation polynomial on a triangle will be used as the approximate value if point (x,y) is an interior point, while the value of a Hermite interpolation function with the form of weighted comb

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3

De Bruin, Marcel G., and Detlef H. Mache. "Independent sets of interpolation nodes or "how to make all sets regular"." Journal of Numerical Analysis and Approximation Theory 41, no. 1 (2012): 42–47. http://dx.doi.org/10.33993/jnaat411-967.

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Hermite-Birkhoff interpolation and Pál-type interpolation have been receiving much attention over the years. Also during the previous 15 years the subject of interpolation in non-uniformly distributed nodes has been looked into. There are, however, not many examples known where lacunary problems (the orders of the derivatives for which data are given, are non-consecutive) are regular. Here lacunary Pál-type interpolation is looked into "the other way around": the interpolation points are given and the orders of the derivatives to be used are derived from the number of points.

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4

Le, Anh N. "Interpolation sets and nilsequences." Colloquium Mathematicum 162, no. 2 (2020): 181–99. http://dx.doi.org/10.4064/cm7937-9-2019.

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5

Pigno, Louis. "Sets of interpolation and small p sets." Colloquium Mathematicum 51, no. 1 (1987): 277–79. http://dx.doi.org/10.4064/cm-51-1-277-279.

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6

Essanhaji, A., and M. Errachid. "Lagrange Multivariate Polynomial Interpolation: A Random Algorithmic Approach." Journal of Applied Mathematics 2022 (March 14, 2022): 1–8. http://dx.doi.org/10.1155/2022/8227086.

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The problems of polynomial interpolation with several variables present more difficulties than those of one-dimensional interpolation. The first problem is to study the regularity of the interpolation schemes. In fact, it is well-known that, in contrast to the univariate case, there is no universal space of polynomials which admits unique Lagrange interpolation for all point sets of a given cardinality, and so the interpolation space will depend on the set Z of interpolation points. Techniques of univariate Newton interpolating polynomials are extended to multivariate data points by different

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7

Calvi, Jean Paul. "A convergence problem for Kergin interpolation." Proceedings of the Edinburgh Mathematical Society 37, no. 1 (1994): 175–83. http://dx.doi.org/10.1017/s0013091500018794.

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Let E, F, G be three compact sets in ℂn. We say that (E, F, G) holds if for any choice of an interpolating array in F and of an analytic function ℂ on G, the Kergjn interpolation polynomial of ℂ exists and converges to ℂ on E. Given two of the three sets, we study how to construct the third in order that (E, F, G) holds.

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8

Rashkovskii, Alexander. "Interpolation of Weighted Extremal Functions." Arnold Mathematical Journal 7, no. 3 (2021): 407–17. http://dx.doi.org/10.1007/s40598-021-00175-x.

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AbstractAn approach to interpolation of compact subsets of $${{\mathbb {C}}}^n$$ C n , including Brunn–Minkowski type inequalities for the capacities of the interpolating sets, was developed in [8] by means of plurisubharmonic geodesics between relative extremal functions of the given sets. Here we show that a much better control can be achieved by means of the geodesics between weighted relative extremal functions. In particular, we establish convexity properties of the capacities that are stronger than those given by the Brunn–Minkowski inequalities.

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9

Bau, David, Hendrik Himmelein, and Christoph Pörschmann. "Comparison of Non-Parametric Interpolation Techniques for Sparsely Measured Binaural Room Impulse Responses." Journal of the Audio Engineering Society 72, no. 7/8 (2024): 479–92. http://dx.doi.org/10.17743/jaes.2022.0150.

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This study investigates different interpolation techniques for spatially upsampling Binaural Room Impulse Responses (BRIRs) measured on a sparse grid of view orientations. In this context, the authors recently presented the Spherical Array Interpolation by Time Alignment (SARITA) method for interpolating spherical microphone array signals with a limited number of microphones, which is adapted for the spatial upsampling of sparse BRIR datasets in the present work. SARITA is compared with two existing nonparametric BRIR-interpolation methods and naive linear interpolation. The study provides a t

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10

Dryanov, Dimiter, and Petar Petrov. "Canonical Sets of BestL1-Approximation." Journal of Function Spaces and Applications 2012 (2012): 1–38. http://dx.doi.org/10.1155/2012/435945.

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In mathematics, the termapproximationusually means either interpolation on a point set or approximation with respect to a given distance. There is a concept, which joins the two approaches together, and this is the concept of characterization of the best approximants via interpolation. It turns out that for some large classes of functions the best approximants with respect to a certain distance can be constructed by interpolation on a point set that does not depend on the choice of the function to be approximated. Such point sets are calledcanonical sets of best approximation. The present pape

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11

Caggiano, J. "Interpolation sets for Fréchet measures." Colloquium Mathematicum 83, no. 2 (2000): 161–72. http://dx.doi.org/10.4064/cm-83-2-161-172.

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12

Korobeinik, Yu F. "Interpolation problems and dense sets." Siberian Mathematical Journal 31, no. 6 (1991): 940–49. http://dx.doi.org/10.1007/bf00970059.

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13

Carvalhaes, C. G. "Spline interpolation on nonunisolvent sets." IMA Journal of Numerical Analysis 33, no. 1 (2012): 370–75. http://dx.doi.org/10.1093/imanum/drs015.

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14

Raubitzek, Sebastian, Thomas Neubauer, Jan Friedrich, and Andreas Rauber. "Interpolating Strange Attractors via Fractional Brownian Bridges." Entropy 24, no. 5 (2022): 718. http://dx.doi.org/10.3390/e24050718.

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We present a novel method for interpolating univariate time series data. The proposed method combines multi-point fractional Brownian bridges, a genetic algorithm, and Takens’ theorem for reconstructing a phase space from univariate time series data. The basic idea is to first generate a population of different stochastically-interpolated time series data, and secondly, to use a genetic algorithm to find the pieces in the population which generate the smoothest reconstructed phase space trajectory. A smooth trajectory curve is hereby found to have a low variance of second derivatives along the

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15

Coburn, James, and Joseph J. Crisco. "Interpolating Three-Dimensional Kinematic Data Using Quaternion Splines and Hermite Curves." Journal of Biomechanical Engineering 127, no. 2 (2004): 311–17. http://dx.doi.org/10.1115/1.1865195.

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Kinematic interpolation is an important tool in biomechanics. The purpose of this work is to describe a method for interpolating three-dimensional kinematic data, minimizing error while maintaining ease of calculation. This method uses cubic quaternion and hermite interpolation to fill gaps between kinematic data points. Data sets with a small number of samples were extracted from a larger data set and used to validate the technique. Two additional types of interpolation were applied and then compared to the cubic quaternion interpolation. Displacement errors below 2% using the cubic quaternio

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16

Kabanko, Mikhail Vladimirovich, and Konstantin Gennadyevich Malyutin. "Interpolation sets in spaces of functions of finite order in half - plane." Ufa Mathematical Journal 16, no. 3 (2024): 40–53. https://doi.org/10.13108/2024-16-3-40.

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We consider free interpolation problems, the study of which was initiated by A.F. Leontiev. We obtain new criterions for the interpolation property of sets in the space of analytic in the upper half - plane functions of finite order. We provide examples of interpolation sets in the space of analytic in the upper half - plane functions of finite order. These examples are similar to interpolation sets in the space of analytic and bounded in the upper half - plane functions. In particular, we provide examples of sets satisfying the Newman condition and uniform Frostman condition.

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17

Mulansky, Bernd, and Marian Neamtu. "Interpolation and approximation from convex sets. II. Infinite-dimensional interpolation." Journal of Computational and Applied Mathematics 119, no. 1-2 (2000): 333–46. http://dx.doi.org/10.1016/s0377-0427(00)00386-1.

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18

López Nicolás, José Alfonso. "Recombination of stable sampling sets and stable interpolation sets in functional quasinormed spaces." Boletim da Sociedade Paranaense de Matemática 42 (May 17, 2024): 1–14. http://dx.doi.org/10.5269/bspm.62925.

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This contribution is aimed in obtaining new results in combining stable sampling sets (respectively, stable interpolation sets) of a given quasinormed space in order to obtain other new ones. We apply these results to Paley-Wiener spaces and. In addition, we study the problem of obtaining a generator system of a given quasinormed space, and obtain conditions for a finite product of subsets of a given quasinormed space to be a generator system, using the interpolation and sampling theory for quasinormed spaces of functions.

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19

PARAMANATHAN, P., and R. UTHAYAKUMAR. "FRACTAL INTERPOLANTS ON THE s-SETS." Fractals 18, no. 03 (2010): 343–48. http://dx.doi.org/10.1142/s0218348x10004993.

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In this paper, we mainly study the s-sets (regular 1-sets), which is the most important fractal in the study of fractal geometry. The regular 1-sets are subsets of countable collection of rectifiable curves. Also we define new real maps on the s-sets by using the methodology based on fractal interpolation functions. In addition, some results are applied to the waveform signals for interpolation.

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20

Jimbo, Toshiya, and Akirp Sakai. "Peak interpolation sets for pseudo-ellipsoids." Complex Variables, Theory and Application: An International Journal 16, no. 2-3 (1991): 131–36. http://dx.doi.org/10.1080/17476939108814475.

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21

Ub⊘e, Jan. "Integral operators on interpolation sets inCn." Complex Variables, Theory and Application: An International Journal 17, no. 1-2 (1991): 105–9. http://dx.doi.org/10.1080/17476939108814500.

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22

Guo, Likang. "The peak-interpolation sets in polydiscs." Complex Variables, Theory and Application: An International Journal 27, no. 2 (1995): 133–42. http://dx.doi.org/10.1080/17476939508814811.

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23

BISHOP, CHRISTOPHER J. "BOUNDARY INTERPOLATION SETS FOR CONFORMAL MAPS." Bulletin of the London Mathematical Society 38, no. 04 (2006): 607–16. http://dx.doi.org/10.1112/s0024609306018583.

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24

Rvachev, V. L., T. I. Sheiko, V. Shapiro, and I. Tsukanov. "Transfinite interpolation over implicitly defined sets." Computer Aided Geometric Design 18, no. 3 (2001): 195–220. http://dx.doi.org/10.1016/s0167-8396(01)00015-2.

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25

Paulsen, Vern I. "Matrix-valued interpolation and hyperconvex sets." Integral Equations and Operator Theory 41, no. 1 (2001): 38–62. http://dx.doi.org/10.1007/bf01202530.

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26

Dyn, Nira, and Michael S. Floater. "Multivariate polynomial interpolation on lower sets." Journal of Approximation Theory 177 (January 2014): 34–42. http://dx.doi.org/10.1016/j.jat.2013.09.008.

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27

Filali, M., and J. Galindo. "Approximable WAP- and LUC-interpolation sets." Advances in Mathematics 233, no. 1 (2013): 87–114. http://dx.doi.org/10.1016/j.aim.2012.09.018.

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28

Gu, Qing. "On interpolation families of wavelet sets." Proceedings of the American Mathematical Society 128, no. 10 (2000): 2973–80. http://dx.doi.org/10.1090/s0002-9939-00-05380-6.

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29

Papush, D. E., and A. M. Russakovskii. "Interpolation on plane sets in C2." Annales de la faculté des sciences de Toulouse Mathématiques 1, no. 3 (1992): 337–62. http://dx.doi.org/10.5802/afst.752.

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30

Polster, B. "Separating sets in interpolation and geometry." aequationes mathematicae 56, no. 3 (1998): 201–15. http://dx.doi.org/10.1007/s000100050056.

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31

Mulansky, Bernd, and Marian Neamtu. "Interpolation and Approximation from Convex Sets." Journal of Approximation Theory 92, no. 1 (1998): 82–100. http://dx.doi.org/10.1006/jath.1996.3107.

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32

Papush, D. E. "Interpolation with discrete sets in Cl." Journal of Soviet Mathematics 59, no. 1 (1992): 666–74. http://dx.doi.org/10.1007/bf01102491.

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33

Nicolás, José Alfonso López. "Irregular stable sampling and interpolation in functional normed spaces." Boletim da Sociedade Paranaense de Matemática 40 (January 24, 2022): 1–13. http://dx.doi.org/10.5269/bspm.45497.

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We define the concepts of stable sampling set and stable interpolation set, uniqueness set and complete interpolation set for a normed space of functions. In addition we will show some relationships between these concepts. The main relationships arise when one wants to reduce an stable sampling set or to extend an stable interpolation set. We will prove that for Banach spaces verifying certain conditions, the complete interpolation sets are precisely the minimal stable sampling sets and are also the maximal stable interpolation sets. Finally we illustrate these results applying them to Paley-W

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34

MacKie, Emma J., Michael Field, Lijing Wang, et al. "GStatSim V1.0: a Python package for geostatistical interpolation and conditional simulation." Geoscientific Model Development 16, no. 13 (2023): 3765–83. http://dx.doi.org/10.5194/gmd-16-3765-2023.

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Abstract. The interpolation of geospatial phenomena is a common problem in Earth science applications that can be addressed with geostatistics, where spatial correlations are used to constrain interpolations. In certain applications, it can be particularly useful to a perform geostatistical simulation, which is used to generate multiple non-unique realizations that reproduce the variability in measurements and are constrained by observations. Despite the broad utility of this approach, there are few open-access geostatistical simulation software applications. To address this accessibility issu

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35

Ignatenko, M. V., and L. A. Yanovich. "On the theory of interpolation of functions on sets of matrices with the Hadamard multiplication." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 58, no. 3 (2022): 263–79. http://dx.doi.org/10.29235/1561-2430-2022-58-3-263-279.

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This article is devoted to the problem of interpolation of functions defined on sets of matrices with multiplication in the sense of Hadamard and is mainly an overview. It contains some known information about the Hadamard matrix multiplication and its properties. For functions defined on sets of square and rectangular matrices, various interpolation polynomials of the Lagrange type, containing both the operation of matrix multiplication in the Hadamard sense and the usual matrix product, are given. In the case of analytic functions defined on sets of square matrices with the Hadamard multipli

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36

Konopatskiy, E. V., N. V. Toropov, and V. V. Shvetsova. "GEOMETRIC METHODS FOR RASTER IMAGE INTERPOLATION IN POINT CALCULUS." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 246 (December 2024): 22–27. https://doi.org/10.14489/vkit.2024.12.pp.022-027.

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The aim of the work is to analyze several methods of interpolation of raster images at their scaling. The idea is to model a composite interpolation response surface by pixels of a raster image and its representation in vector form with subsequent calculation of intermediate color values between interpolation node points. To verify and compare several geometric interpolation algorithms, a method of numerical evaluation of the degree of similarity of geometric objects in the form of two points sets based on the use of the coefficient of determination is used. Parabolic curves of second and thir

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37

Phung, V. M., V. T. Nguyen та H. L. Dinh. "Combining interpolation schemes and Lagrange interpolation on the unit sphere in ℝ N + 1". Ukrains’kyi Matematychnyi Zhurnal 74, № 4 (2022): 542–59. http://dx.doi.org/10.37863/umzh.v74i4.6512.

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UDC 517.9 We study Lagrange interpolation in ℝ N and on the unit sphere in ℝ N + 1 . We show that sequences of unisolvent sets can be combined to get other sequences of unisolvent sets such that the existence of the limits is preserved. Moreover, the limiting operators keep the interpolation conditions under the combining process.

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38

Vâjâitu, Viorel. "An interpolation property of locally Stein sets." Publicacions Matemàtiques 63 (July 1, 2019): 715–25. http://dx.doi.org/10.5565/publmat6321909.

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39

Nikolov, Nikolai, and Peter Pflug. "Simultaneous Approximation and Interpolation on Arakelian Sets." Canadian Mathematical Bulletin 50, no. 1 (2007): 123–25. http://dx.doi.org/10.4153/cmb-2007-012-9.

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40

Guo, Likang. "The peak-interpolation sets in product domains." Complex Variables, Theory and Application: An International Journal 27, no. 2 (1995): 143–62. http://dx.doi.org/10.1080/17476939508814812.

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41

Han, Deguang. "Interpolation operators associated with sub-frame sets." Proceedings of the American Mathematical Society 131, no. 1 (2002): 275–84. http://dx.doi.org/10.1090/s0002-9939-02-06658-3.

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42

Amo, Enrique de, Manuel Díaz Carrillo, and Juan Fernández Sánchez. "PCF self-similar sets and fractal interpolation." Mathematics and Computers in Simulation 92 (June 2013): 28–39. http://dx.doi.org/10.1016/j.matcom.2013.04.017.

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43

de Boor, Carl. "Multivariate polynomial interpolation: conjectures concerning GC-sets." Numerical Algorithms 45, no. 1-4 (2007): 113–25. http://dx.doi.org/10.1007/s11075-006-9062-2.

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44

Costabile, F. A., F. Dell’Accio, and F. Di Tommaso. "Complementary Lidstone interpolation on scattered data sets." Numerical Algorithms 64, no. 1 (2012): 157–80. http://dx.doi.org/10.1007/s11075-012-9659-6.

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45

Kaijser, Sten. "Interpolation of Banach algebras and open sets." Integral Equations and Operator Theory 41, no. 2 (2001): 189–222. http://dx.doi.org/10.1007/bf01295305.

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46

Cendes, Zoltan, and Steven Wong. "C1 Quadratic Interpolation over Arbitrary Point Sets." IEEE Computer Graphics and Applications 7, no. 11 (1987): 8–16. http://dx.doi.org/10.1109/mcg.1987.277064.

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47

Luor, Dah-Chin. "Fractal interpolation functions for random data sets." Chaos, Solitons & Fractals 114 (September 2018): 256–63. http://dx.doi.org/10.1016/j.chaos.2018.06.033.

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48

Faina, Loris. "Interpolation of Level Sets for Equimeasurable Functions." Journal of Mathematical Analysis and Applications 221, no. 1 (1998): 349–63. http://dx.doi.org/10.1006/jmaa.1997.5901.

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49

Kalton, N. "On vector-valued inequalities for Sidon sets and sets of interpolation." Colloquium Mathematicum 64, no. 2 (1993): 233–44. http://dx.doi.org/10.4064/cm-64-2-233-244.

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50

Leetma, Evely. "QUASI-INTERPOLATION BY SPLINES ON THE UNIFORM KNOT SETS." Mathematical Modelling and Analysis 12, no. 1 (2007): 107–20. http://dx.doi.org/10.3846/1392-6292.2007.12.107-120.

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In the case of uniform grids, the error of the spline interpolant of a function defined on R has been well estimated. On the basis of the spline interpolation formula for functions defined on R we derive quasi‐interpolation formulae for functions defined on R or in a vicinity of a bounded interval, say [0,1], and we estimate the difference between the interpolant and the quasi‐interpolants.

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