• Corpus ID: 18178738

The Spectral Basis and Rational Interpolation

  title={The Spectral Basis and Rational Interpolation},
  author={Garret Sobczyk},
  journal={arXiv: Numerical Analysis},
  • G. Sobczyk
  • Published 18 February 2006
  • Mathematics
  • arXiv: Numerical Analysis
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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