Decay bounds and linear scaling algorithms for approximating functions of band matrices
نویسندگان
چکیده
We establish decay bounds for the entries of f(A) where A is a banded (more generally, sparse) n × 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 banded approximations to f(A), resulting in algorithms that under appropriate conditions have linear complexity in the matrix size n. Applications to various types of problems are discussed and illustrated by numerical examples.
منابع مشابه
DECAY BOUNDS AND O(n) ALGORITHMS FOR APPROXIMATING FUNCTIONS OF SPARSE MATRICES
We establish decay bounds for the entries of f(A), where A is a sparse (in particular, banded) n×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 c...
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