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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(More)
Motivated by applications in quantum chemistry and solid state physics, we apply general results from approximation theory and matrix analysis to the study of the decay properties of spectral projectors associated with large and sparse Hermitian matrices. Our theory leads to a rigorous proof of the exponential off-diagonal decay (" nearsightedness ") for(More)
We consider a generalization of the constrained shortest path problem, in which we forbid certain pairs of edges to appear consecutively on a feasible path. This problem has applications in robotics and optimal mission planning. We propose a dynamical programming heuristic for this problem and show computational results for an application in routing an(More)
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(More)
Motivated by applications in quantum chemistry and solid state physics, we apply general results from approximation theory and matrix analysis to the study of the decay properties of spectral projectors associated with large and sparse Hermitian matrices. Our theory leads to a rigorous proof of the exponential off-diagonal decay ('nearsightedness') for the(More)
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