ISSN:
1572-9044
Keywords:
Periodic pseudodifferential equations
;
pre-wavelets
;
biorthogonal wavelets
;
generalized Petrov-Galerkin schemes
;
wavelet representation
;
atomic decomposition
;
Calderón-Zygmund operators
;
matrix compression
;
error analysis
;
65F35
;
65J10
;
65N30
;
65N35
;
65R20
;
47A20
;
47G30
;
45P05
;
41A25
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract This is the second part of two papers which are concerned with generalized Petrov-Galerkin schemes for elliptic periodic pseudodifferential equations in ℝ n . This setting covers classical Galerkin methods, collocation, and quasi-interpolation. The numerical methods are based on a general framework of multiresolution analysis, i.e. of sequences of nested spaces which are generated by refinable functions. In this part, we analyse compression techniques for the resulting stiffness matrices relative to wavelet-type bases. We will show that, although these stiffness matrices are generally not sparse, the order of the overall computational work which is needed to realize a certain accuracy is of the formO(N(logN) b ), whereN is the number of unknowns andb ≥ 0 is some real number.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02072014
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