## Abstract

Let m be a polynomial satisfying some mild conditions. Given a set R ⊂ C, a continuous function f on R and its best approximation p*_{n- 1} from II_{n} with respect to the maximum norm, we show that p*_{n} p*_{n} is a best approximation to f o _{m} on the inverse polynomial image 5 of R, i.e. _{m}(S) = R, where the extremal signature is given explicitly. A similar result is presented for constrained Chebyshev polynomial approximation. Finally, we apply the obtained results to the computation of the convergence rate of Krylov subspace methods when applied to a preconditioned linear system. We investigate pairs of preconditioners where the eigenvalues are contained in sets 5 and R, respectively, which are related by _{m}(S) = R.

Original language | English |
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Journal | Electronic Transactions on Numerical Analysis |

Volume | 12 |

Pages (from-to) | 205-215 |

Number of pages | 11 |

ISSN | 1068-9613 |

Publication status | Published - 01.12.2001 |