Finding the interpolation function of a given set of nodes is an important problem in scientific computing. In this work a kind of localization is introduced using the radial basis functions which finds a sufficiently smooth solution without consuming large amount of time and computer memory. Some examples will be presented to show the efficiency of the new method., {"references":["M. D. Buhmann, Spectral convergence of multiquadric interpolation,\nProc. Edinburg Math. Soc. 36 (1993) 319-333.","M. D. Buhmann, Radial basis functions, Combridge University Press,\nCombridge, 2003.","R. E. Carlson, T. A. Foley, The parameter r2 in multiquadric interpolation,\nProc. Edinburg Math. Soc. 36 (1993) 319-333.","B. Fornberg, N. Flyer, Accuracy of radial basis function interpolation and\nderivative approximations on 1-D infinite grids, Adv. Comput. Math. 23\n(2005) 5-20.","B. Fornberg, T. Driscoll, G.Wright, Charles, Observations on the behavior\nof radial basis function approxiamtions near boundaries, Comput. Math.\nAppl. 43 (2002) 473-490.","W. R. Madych, S. A. Nelson, Error bounds for multiquadric interpolation,\nin: C. Chui, L. Schumaker, J. Ward(Eds.), Approximation Theory VI,\nAcademic Press, New York, 1989, pp. 413-416.","W. R. Madych, S. A. Nelson, Multivariate interpolation and conditionally\npositive definite functions, ii, Math. Comp. 4 (1990) 211-230.","W. R. Madych, Miscellaneous error bounds for multiquadric and related\ninterpolators, Comput. Math. Appl. 24 (1992) 121-138.","M. Powell, The theory of radial basis function approximation in 1990,\nin: W. Light(Ed.), Advances in Numerical Analysis, vol. II: Wavelets,\nSubdivision Algorithms and Radial Functions, 1990.\n[10] R. Platte, T. Driscoll, Computing eigenmodes of elliptic operators using\nradial basis functions, Comput. Math. Appl. 48 (2004) 561-576.\n[11] S. Rippa, An algorithm for selecting a good parameter c in radial basis\nfunction interpolation, Adv. Comput. Math. 11 (1999) 193-210.\n[12] R. Platte, T. Driscoll, Polynomials and potential theory for Gaussian\nradial basis function interpolation, SIAM J. Numer. Anal. 43 (2005) 750-\n766.\n[13] S. A. Sarra, Adiptive radial basis function method for time dependent\npartial differential equations, Applied Numerical Mathemetics 54 (2005)\n79-94.\n[14] R. Schaback, Error estimates and condition numbers for radial basis\nfunction interpolation, Adv. Comput. Math. 3 (1995) 251-264.\n[15] I. J. Schoenberg, Metric spaces and comletely monotone functions, Ann.\nMath. 39 (1938) 811-841.\n[16] H. Wendland, Gaussian interpolation revisited, in trend in Approximation\nTheory, K.Kopotun, T. Lyche, and N. Neamtu, eds., Vanderbilt\nUniversity Press, nashville, TN, 2001, 1-10.\n[17] J. Yoon, Spectral approximation orders of radial basis function interpolation\non the Sobolov space, SIAM J. Math. Anal. 33 (2001) 946-958."]}