Geodesic
Decay bounds and \(O(n)\) algorithms for approximating functions of sparse matrices
Electronic transactions on numerical analysis, Tome 28 (2008)
We establish decay bounds for the entries of f (A), where A is a sparse (in particular, banded) n $\times n$ diagonalizable matrix and f is smooth on a subset of the complex plane containing the spectrum of A. Combined with techniques from approximation theory, the bounds are used to compute sparse (or banded) approximations to f (A), resulting in algorithms that under appropriate conditions have linear complexity in the matrix dimension.
Classification : 65F10, 65F30, 15A
Keywords: matrix functions, sparse and banded matrices, decay rates, linear time algorithms, Chebyshev polynomials, Faber polynomials, density matrix, trace, determinant 
@article{ETNA_2008__28__a11,
     author = {Benzi,  Michele and Razouk,  Nader},
     title = {Decay bounds and {\(O(n)\)} algorithms for approximating functions of sparse matrices},
     journal = {Electronic transactions on numerical analysis},
     year = {2008},
     volume = {28},
     zbl = {1171.65034},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__28__a11/}
}
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%A Razouk,  Nader
%T Decay bounds and \(O(n)\) algorithms for approximating functions of sparse matrices
%J Electronic transactions on numerical analysis
%D 2008
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%U http://geodesic.mathdoc.fr/item/ETNA_2008__28__a11/
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%F ETNA_2008__28__a11
Benzi,  Michele; Razouk,  Nader. Decay bounds and \(O(n)\) algorithms for approximating functions of sparse matrices. Electronic transactions on numerical analysis, Tome 28 (2008). http://geodesic.mathdoc.fr/item/ETNA_2008__28__a11/