روش افراز واحد چندجمله‌ای؛ ابزاری کارامد در تقریب توابع

[1] D. Braess, Nonlinear Approximation Theory, Springer, New York, 1986.
[2] M. A. Darani,The RBF partition of unity method for solving the Klein-Gordon equation, Engineering with Computers, 37
(2021) 795.
[3] C. De Boor, A Practical Guide to Splines, Applied Mathematical Sciences, Springer, Berlin, 2001.
[4] S. De Marchi, A. Martínez, and E. Perracchione, Fast and stable rational RBF-based partition of unity interpolation, J. Comput.
Appl. Math., 349 (2019) 331–343.
[5] G. E. Fasshauer, Meshfree Approximations Methods with Matlab, World Scientific, Singapore, 2007.
[6] R. Franke, Scattered data interpolation: tests of some methods, Math. Comp., 48 (1982) 181–200.
[7] P. Gonnet, R. Pachon and L. N. Trefethen, Robust rational interpolation and least-squares, Electron. Trans. Numer. Anal., 38
(2011) 146–167.
[8] M. Junk, Do finite volume methods need a mesh?, in Meshfree Methods for Partial Differential Equations, M. Griebel and
M. A. Schweitzer, eds., Springer, New York, 2003, 223–238.
[9] E. Larsson, V. Shcherbakov and A. Heryudono, A least squares radial basis function partition of unity method for solving
PDEs, SIAM J. Sci. Comput., 39 (2017) A2538–A2563.
[10] J. M. Melenk and I. Babuška, The partition of unity finite element method: Basic theory and applications, Comput. Methods
Appl. Mech. Engrg., 139 (1996) 289–314.
[11] D. Mirzaei, The direct radial basis function partition of unity (D-RBF-PU) method for solving PDEs, SIAM J. Sci. Comput.,
43 (2021) A54–A83.
[12] Y. Nakatsukasa, O. Sète, and L. N. Trefethen, The AAA Algorithm for Rational Approximation, SIAM J. Sci. Comput., 40
(2018) A1494–A1522.
[13] A. Safdari-Vaighani, A. Heryudono, and E. Larsson, A radial basis function partition of unity collocation method for
convection—diffusion equations arising in financial applications, J. Sci. Comput., 46 (2015) 341–367.
[14] V. Shcherbakov, Radial basis function partition of unity operator splitting method for pricing multi-asset American options,
BIT, 56 (2016) 1401–1423.
[15] D. Shepard, A two-dimensional interpolation function for irregularly-spaced data, in Proceedings of the 23th National Con-ference ACM, 1968, 517–523.
[16] J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, Texts in Applied Mathematics, Springer, New York, 2002.
[17] L. N. Trefethen, Approximation Theory and Approximation Practice, SIAM, Philadelphia, 2013.
[18] H. Wendland, Fast evaluation of radial basis functions: methods based on partition of unity, in Approximation Theory, X:
Wavelets, Splines, and Applications (Nashville, TN., 2002), Vanderbilt University Press, 473–483.
[19] H. Wendland, Scattered Data Approximation, Cambridge University Press, Cambridge, 2005.

[20] D. Mirzaei, Advanced Numerical Analysis, Isfahan University Press, Isfahan, 2014.