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Calculating elements of matrix functions using divided differences
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DOI：10.1016/j.cpc.2021.108219.png)
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摘要
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We introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We showcase our approach by calculating the matrix elements of the exponential of a transverse-field Ising model and evaluating quantum transition amplitudes for large many-body Hamiltonians of sizes up to 2(64)x2(64) on a single workstation. We also discuss the application of the method to matrix inverses. We relate and compare our method to the state-of-the-art and demonstrate its advantages. We also discuss practical applications of our method. (C) 2021 Elsevier B.V. All rights reserved.
Keyword:
Matrix functions
Divided differences
Off-diagonal series expansion
Matrix exponential
Transverse-field Ising model
Quantum transition amplitudes
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期刊
IF:
3.4
论文数:
1.2W
被引数:
3.7W
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