# Effective solution of a linear system with Chebyshev coefficients

Title | Effective solution of a linear system with Chebyshev coefficients |

Publication Type | Journal Article |

Year of Publication | 2009 |

Authors | Kujan, Petr, Martin Hromčík, and Michael Šebek |

Journal | Integral Transforms and Special Functions |

Volume | 20 |

Issue | 8 |

Page | 619-628 |

Abstract | This paper presents an efficient algorithm for a special triangular linear system with Chebyshev coefficients. We present two methods of derivations, the first is based on formulae where the nth power of x is solved as the sum of Chebyshev polynomials and modified for a linear system. The second deduction is more complex and is based on the Gauss-Banachiewicz decomposition for orthogonal polynomials and the theory of hypergeometric functions which are well known in the context of orthogonal polynomials. The proposed procedure involves O(nm) operations only, where n is matrix size of the triangular linear system L and m is number of the nonzero elements of vector b. Memory requirements are O(m), and no recursion formula is needed. The linear system is closely related to the optimal pulse-wide modulation problem. |

URL | http://dx.doi.org/10.1080/10652460902727938 |

DOI | 10.1080/10652460902727938 |