Geodesic
High-order finite difference schemes and Toeplitz based preconditioners for elliptic problems
Electronic transactions on numerical analysis, Tome 11 (2000), pp. 55-84
In this paper we are concerned with the spectral analysis of the sequence of preconditioned matrices P - 1 n (a, m, k)$An(a, m, k)$n, where $An(a, m, k)$ is the n $\times n$ symmetric matrix coming from a high-order Finite Difference discretization of the problem

$###$

dk

$###$

###

$ - )k dk dxk dxk ds $

###$ u(x) = 0$ s = 0, . . . , k

$###$

- 1.
Classification : 65N22, 65F10, 15A12
Keywords: finite differences, Toeplitz and vandermonde matrices, clustering and preconditioning, ergodic theorems, spectral distribution 
@article{ETNA_2000__11__a4,
     author = {Serra Capizzano,  Stefano and Tablino Possio,  Cristina},
     title = {High-order finite difference schemes and {Toeplitz} based preconditioners for elliptic problems},
     journal = {Electronic transactions on numerical analysis},
     pages = {55--84},
     year = {2000},
     volume = {11},
     zbl = {0985.65129},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2000__11__a4/}
}
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%A Tablino Possio,  Cristina
%T High-order finite difference schemes and Toeplitz based preconditioners for elliptic problems
%J Electronic transactions on numerical analysis
%D 2000
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%G en
%F ETNA_2000__11__a4
Serra Capizzano,  Stefano; Tablino Possio,  Cristina. High-order finite difference schemes and Toeplitz based preconditioners for elliptic problems. Electronic transactions on numerical analysis, Tome 11 (2000), pp. 55-84. http://geodesic.mathdoc.fr/item/ETNA_2000__11__a4/