Stability analysis of algorithms for solving confluent Vandermonde-like systems

  title={Stability analysis of algorithms for solving confluent Vandermonde-like systems},
  author={Nicholas John Higham},
  journal={SIAM Journal on Matrix Analysis and Applications},
  • N. Higham
  • Published 1990
  • Mathematics
  • SIAM Journal on Matrix Analysis and Applications
A confluent Vandermonde-like matrix $P(\alpha _0 ,\alpha _1 , \cdots ,\alpha _n )$ is a generalisation of the confluent Vandermonde matrix in which the monomials are replaced by arbitrary polynomials. For the case where the polynomials satisfy a three-term recurrence relation algorithms for solving the systems $Px = b$ and $P^T a = f$ in $O(n^2 )$ operations are derived. Forward and backward error analyses that provide bounds for the relative error and the residual of the computed solution are… Expand
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