TY  - BOOK
AU  - Börm,Steffen
AU  - Börm,Steffen
TI  - Efficient Numerical Methods for Non-local Operators: ℋ2-Matrix Compression, Algorithms and Analysis  Corrected 2nd printing, September 2013 
T2  - EMS Tracts in Mathematics (ETM)
SN  - 9783037195918
PY  - 2010///
CY  - Zuerich, Switzerland
PB  - European Mathematical Society Publishing House
KW  - Calculus & mathematical analysis
KW  - bicssc
KW  - Numerical analysis
KW  - msc
N1  - Restricted to subscribers
N2  - Hierarchical matrices present an efficient way of treating dense matrices  that arise in the context of integral equations, elliptic partial  differential equations, and control theory.    While a dense n × n matrix in standard representation requires  n2 units of storage, a hierarchical matrix can approximate the  matrix in a compact representation requiring only O(nk log n) units  of storage, where k is a parameter controlling the accuracy.  Hierarchical matrices have been successfully applied to approximate  matrices arising in the context of boundary integral methods, to  construct preconditioners for partial differential equations, to  evaluate matrix functions and to solve matrix equations used in control  theory.  ℋ2-matrices  offer a refinement of hierarchical matrices: using a  multilevel representation of submatrices, the efficiency can be  significantly improved, particularly for large problems.      This books gives an introduction to the basic concepts and presents a  general framework that can be used to analyze the complexity and  accuracy of ℋ2-matrix techniques.  Starting from basic ideas of numerical linear  algebra and numerical analysis, the theory is developed in a straightforward and systematic way, accessible to advanced students and researchers  in numerical mathematics and scientific computing. Special techniques are only required  in isolated sections, e.g., for certain classes of model problems
UR  - https://doi.org/10.4171/091
UR  - http://www.ems-ph.org/img/books/börm_mini.jpg
ER  -