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Technical Report

HLIBpro User Manual

Ronald Kriemann


HLIBpro is a software library implementing hierarchical matrices or H-matrices for short. This type of matrices provides a technique to represent various full matrices in a data-sparse format and furthermore, allows usual matrix arithmetic, e.g. matrix-vector multiplication, matrix multiplication and inversion, with almost linear complexity. Examples of matrices, which can be represented by H-matrices stem from the area of partial differential or integral equations.

Beside the standard arithmetic mentioned above, HLIBpro also provides additional algorithms for decomposing matrices, e.g. LU-factorisation and for solving linear equation systems with various direct or iterative methods. Furthermore, it contains methods for directly converting a dense operator into an H-matrix without constructing the corresponding dense matrix.

MSC Codes:
68N01, 68W25, 68W10, 65F05, 65F30, 65F50
hierarchical matrices, Dense Matrices, sparse matrices