Change of basis in polynomial interpolation
Walter Gander · Numerical Linear Algebra with Applications · 2005
Abstract Several representations for the interpolating polynomial exist: Lagrange, Newton, orthogonal polynomials, etc. Each representation is characterized by some basis functions. In this paper we investigate the transformations between the basis functions which map a specific representation to another. We show that for this purpose the LU ‐ and the QR ‐decomposition of the Vandermonde matrix play a crucial role. Copyright © 2005 John Wiley & Sons, Ltd.