Wolfgang Hackbusch

Multi-grid methods and applications

1. Preliminaries.- 2. Introductory Model Problem.- 3. General Two-Grid Method.- 4. General Multi-Grid Iteration.- 5. Nested Iteration Technique.- 6. Convergence of the Two-Grid Iteration.- 7. Convergence of the Multi-Grid Iteration.- 8. Fourier Analysis.- 9. Nonlinear Multi-Grid Methods.- 10. Singular Perturbation Problems.- 11. Elliptic Systems.- 12. Eigenvalue Problems and Singular Equations.- 13. Continuation Techniques.- 14. Extrapolation and Defect Correction Techniques.- 15. Local Techniques.- 16. The Multi-Grid Method of the Second Kind.

A sparse matrix arithmetic based on H -matrices. Part I: introduction to H -matrices

Abstract.A class of matrices (

Iterative Solution of Large Sparse Systems of Equations

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On the fast matrix multiplication in the boundary element method by panel clustering

-matrices) is introduced which have the following properties. (i) They are sparse in the sense that only few data are needed for their representation. (ii) The matrix-vector multiplication is of almost linear complexity. (iii) In general, sums and products of these matrices are no longer in the same set, but their truncations to the

Tensor spaces and numerical tensor calculus

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Construction and arithmetics of H -matrices

-matrix format are again of almost linear complexity. (iv) The same statement holds for the inverse of an

Introduction to hierarchical matrices with applications

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Elliptic differential equations : theory and numerical treatment

-matrix.This paper is the first of a series and is devoted to the first introduction of the

A New Convergence Proof for the Multigrid Method Including the V-Cycle

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On first and second order box schemes

-matrix concept. Two concret formats are described. The first one is the simplest possible. Nevertheless, it allows the exact inversion of tridiagonal matrices. The second one is able to approximate discrete integral operators.