Block Based Newton-Like Blending Interpolation (Journal of Computational Mathematics, 2006)
Newton's polynomial interpolation may be the favourite linear interpolation in the sense that it is built up by means of the divided differences which can be calculated recursively and produce useful intermediate results. However, Newton interpolation is in fact point based interpolation since a new interpolating polynomial with one more degree is obtained by adding a new support point into the current set of support points once at a time. In this paper we extend the point based interpolation to the block based interpolation. Inspired by the idea of the modern architectural design, we first divide the original set of support points into some subsets (blocks), then construct each block by using whatever interpolation means, linear or rational and finally assemble these blocks by Newton's method to shape the whole interpolation scheme. Clearly our method offers many flexible interpolation schemes for choices which include the classical Newton's polynomial interpolation as its special case. A bivariate analogy is also discussed and numerical examples are given to show the effectiveness of our method.
Keywords: Interpolation; Block based divided differences; Blending method.