## Efficient Numerical Methods for Non-local Operators: H2-matrix Compression, Algorithms and Analysis |

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### Contents

Introduction | 1 |

Model problem | 9 |

Hierarchical matrices | 28 |

Application to integral operators | 74 |

Orthogonal cluster bases and matrix projections | 163 |

Compression | 211 |

A priori matrix arithmetic | 280 |

A posteriori matrix arithmetic | 332 |

Application to elliptic partial differential operators | 363 |

Applications | 387 |

421 | |

427 | |

### Other editions - View all

Efficient Numerical Methods for Non-local Operators: H2-matrix Compression ... Steffen Börm No preview available - 2010 |

### Common terms and phrases

According to Lemma admissibility condition admissible block cluster admissible leaf Algorithm 18 apply approximation error backward transformation bases block cluster tree Chapter complexity compute conclude construct convergence Corollary corresponding defined Definition Due to Lemma efficient end for end equation error estimate factorization Frobenius norm G 7j G R>o given hierarchical matrices holds implies inadmissible index set interpolation operator introduced J^-matrix kernel function L2-norm Lagrange polynomials leaf clusters Lemma level(r low-rank approximations M2-matrix multiplication nested cluster basis number of operations orthogonal matrix polynomial preconditioner Proof rank distribution recursion representation result satisfying Section semi-uniform matrix singular value decomposition sons sons(r space spectral norm storage requirements submatrices t e Tj Ta,Ix Tajx Taylor expansion teTj Theorem TmjxJC total cluster basis transfer matrices units of storage variable-order vector XtXXs yields