Hierarchical Matrices
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21. Max Planck Institute for Mathematics in the Sciences, Leipzig, (2003)

These are the lecture notes for a winter school on the subject of hierarchical matrices. They give an introduction both to the basic theory of H-matrices, including complexity estimates and error estimates, and to the practice, i.e., the efficient implementation of the construction of cluster trees and block cluster trees, the approximation of finite element and boundary element matrices and the H-matrix arithmetic operations. A program library containing all the routines from these notes and many extensions for more sophisticated applications can be obtained from the authors.
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