02717nam a22003375a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084001500184100002900199245018800228260008200416300003400498336002600532337002600558338003600584347002400620490004000644506006600684520145900750650004502209650002802254856003202282856006502314125-101201CH-001817-320101201234500.0a fot ||| 0|cr nn mmmmamaa101201e20101201sz fot ||| 0|eng d a978303719591870a10.4171/0912doi ach0018173 7aPBK2bicssc a65-xx2msc1 aBörm, Steffen,eauthor.10aEfficient Numerical Methods for Non-local Operatorsh[electronic resource] :bℋ2-Matrix Compression, Algorithms and Analysis Corrected 2nd printing, September 2013 /cSteffen Börm3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2010 a1 online resource (441 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aEMS Tracts in Mathematics (ETM)v141 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aHierarchical 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.07aCalculus & mathematical analysis2bicssc07aNumerical analysis2msc40uhttps://doi.org/10.4171/091423cover imageuhttps://www.ems-ph.org/img/books/börm_mini.jpg