Decay estimates of discretized Green’s functions for Schrödinger type operators
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2016-08-01
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© 2016, Science China Press and Springer-Verlag Berlin Heidelberg.For a sparse non-singular matrix A, generally A−1 is a dense matrix. However, for a class of matrices, A−1 can be a matrix with off-diagonal decay properties, i.e., |Aij−1| decays fast to 0 with respect to the increase of a properly defined distance between i and j. Here we consider the off-diagonal decay properties of discretized Green’s functions for Schrödinger type operators. We provide decay estimates for discretized Green’s functions obtained from the finite difference discretization, and from a variant of the pseudo-spectral discretization. The asymptotic decay rate in our estimate is independent of the domain size and of the discretization parameter. We verify the decay estimate with numerical results for one-dimensional Schrödinger type operators.
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Lin, L, and J Lu (2016). Decay estimates of discretized Green’s functions for Schrödinger type operators. Science China Mathematics, 59(8). pp. 1561–1578. 10.1007/s11425-016-0311-4 Retrieved from https://hdl.handle.net/10161/14112.
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Jianfeng Lu
Jianfeng Lu is an applied mathematician interested in mathematical analysis and algorithm development for problems from computational physics, theoretical chemistry, materials science, machine learning, and other related fields.
More specifically, his current research focuses include:
High dimensional PDEs; generative models and sampling methods; control and reinforcement learning; electronic structure and many body problems; quantum molecular dynamics; multiscale modeling and analysis.
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