BIVARIATE POLYNOMIAL INTERPOLATION BASED ON LINE INTEGRALS
DOI:
https://doi.org/10.18173/2354-1059.2025-0033Keywords:
Polynomial interpolation, Mean-value interpolation, Line integralAbstract
We study bivariate polynomial interpolation based on line integrals over line segments connecting two points on two fixed straight lines in the plane. We provide a characterization of the sets of segments that uniquely determine the interpolation polynomial. We also construct illustrative examples for specific cases.
References
[1] Bojanov B & Xu Y, (2003). On polynomial interpolation of two variables. Journal of Approximation Theory, 120, 267–282.
[2] Bos L, (1991). On certain configurations of points in ℝn which are unisolvent for polynomial interpolation. Journal of Approximation Theory, 64, 271–280.
[3] Calvi JP, (2005). Intertwining unisolvent arrays for multivariate Lagrange interpolation. Advances in Computational Mathematics, 23, 393–414.
[4] Chung KC & Yao TH, (1977). On lattices admitting unique Lagrange interpolations. SIAM Journal on Numerical Analysis, 14, 735–743.
[5] Logan B & Shepp L, (1975). Optimal reconstruction of a function from its projections. Duke Mathematical Journal, 42, 645–659.
[6] Marr R, (1974). On the reconstruction of a function on a circular domain from a sampling of its line integrals. Journal of Mathematical Analysis and Applications, 45, 357–374.
[7] Xu Y, (2006). A new approach to the reconstruction of images from Radon projections. Advances in Applied Mathematics, 36, 388–420.
[8] Bojanov B & Georgieva I, (2004). Interpolation by bivariate polynomials based on Radon projections. Studia Mathematica, 162, 141–160.
[9] Bojanov B & Xu Y, (2005). Reconstruction of a bivariate polynomial from its Radon projections. SIAM Journal on Numerical Analysis, 37, 238–250.
[10] Nguyen AN, Nguyen VK, Tang VL & Phung VM, (2024). Multivariate polynomial interpolation based on Radon projections. Numerical Algorithms. https://doi.org/10.1007/s11075-024-01938-1
