The Spectral Basis and Rational Interpolation

Details The Spectral Basis and Rational Interpolation The Spectral Basis and Rational Interpolation

2006-02-18

arxiv.org/abs/math/0602405v1

Mathematics

Numerical Analysis

8 pages, 2 figures

Scientific paper

The Euclidean Algorithm is the often forgotten key to rational approximation techniques, including Taylor, Lagrange, Hermite, osculating, cubic spline, Chebyshev, Pade and other interpolation schemes. A unified view of these various interpolation techniques is eloquently expressed in terms of the concept of the spectral basis of a factor ring of polynomials. When these methods are applied to the minimal polynomial of a matrix, they give a family of rational forms of functions of that matrix.

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