Combining interpolation schemes and Lagrange interpolation on the unit sphere in ℝ N + 1

Abstract

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.