### Abstract

Original language | English |
---|---|

Pages (from-to) | 1157-1170 |

Number of pages | 14 |

Journal | Linear Algebra and its Applications |

Volume | 435 |

Issue number | 1 |

Early online date | 30 Mar 2011 |

DOIs | |

Publication status | Published - 2011 |

### Fingerprint

### Keywords

- inverse of lower triangular Toeplitz matrix
- Abel equation
- Brunner’s conjecture

### Cite this

*Linear Algebra and its Applications*,

*435*(1), 1157-1170. https://doi.org/10.1016/j.laa.2011.02.044

}

*Linear Algebra and its Applications*, vol. 435, no. 1, pp. 1157-1170. https://doi.org/10.1016/j.laa.2011.02.044

**Uniform bounds on the 1-norm of the inverse of lower triangular Toeplitz matrices.** / Liu, X.; McKee, S.; Yuan, J.Y.; Yuan, Y.X.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Uniform bounds on the 1-norm of the inverse of lower triangular Toeplitz matrices

AU - Liu, X.

AU - McKee, S.

AU - Yuan, J.Y.

AU - Yuan, Y.X.

PY - 2011

Y1 - 2011

N2 - A uniform bound on the 1-norm is given for the inverse of a lower triangular Toeplitz matrix with non-negative monotonically decreasing entries whose limit is zero. The new bound is sharp under certain specified constraints. This result is then employed to throw light upon a long standing open problem posed by Brunner concerning the convergence of the one-point collocationmethod for the Abel equation. In addition, the recent conjecture of Gauthier et al. is proved.

AB - A uniform bound on the 1-norm is given for the inverse of a lower triangular Toeplitz matrix with non-negative monotonically decreasing entries whose limit is zero. The new bound is sharp under certain specified constraints. This result is then employed to throw light upon a long standing open problem posed by Brunner concerning the convergence of the one-point collocationmethod for the Abel equation. In addition, the recent conjecture of Gauthier et al. is proved.

KW - inverse of lower triangular Toeplitz matrix

KW - Abel equation

KW - Brunner’s conjecture

UR - http://www.scopus.com/inward/record.url?scp=79958825418&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2011.02.044

DO - 10.1016/j.laa.2011.02.044

M3 - Article

VL - 435

SP - 1157

EP - 1170

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

SN - 0024-3795

IS - 1

ER -