By Mario Bebendorf
Hierarchical matrices are a good framework for large-scale totally populated matrices coming up, e.g., from the finite point discretization of resolution operators of elliptic boundary price difficulties. as well as storing such matrices, approximations of the standard matrix operations will be computed with logarithmic-linear complexity, that are exploited to setup approximate preconditioners in a good and handy manner. in addition to the algorithmic elements of hierarchical matrices, the most objective of this publication is to provide their theoretical background.
The booklet comprises the prevailing approximation concept for elliptic difficulties together with partial differential operators with nonsmooth coefficients. in addition, it provides in complete aspect the adaptive pass approximation procedure for the effective remedy of indispensable operators with non-local kernel services. the idea is supported via many numerical experiments from actual applications.
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Extra resources for Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems: 63 (Lecture Notes in Computational Science and Engineering)
Hierarchical Matrices: A Means to Efficiently Solve Elliptic Boundary Value Problems: 63 (Lecture Notes in Computational Science and Engineering) by Mario Bebendorf