By Mario Bebendorf

Hierarchical matrices are a good framework for large-scale totally populated matrices coming up, e.g., from the finite aspect discretization of resolution operators of elliptic boundary worth difficulties. as well as storing such matrices, approximations of the standard matrix operations will be computed with logarithmic-linear complexity, which are exploited to setup approximate preconditioners in an effective and handy method. along with the algorithmic points of hierarchical matrices, the most target of this ebook is to provide their theoretical background.

The ebook comprises the present approximation conception for elliptic difficulties together with partial differential operators with nonsmooth coefficients. in addition, it provides in complete element the adaptive move approximation technique for the effective remedy of critical operators with non-local kernel services. the speculation is supported via many numerical experiments from actual applications.

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