arXiv Open Access 2021

Calculating elements of matrix functions using divided differences

Lev Barash Stefan Güttel Itay Hen

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Abstrak

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 $2^{64} \times 2^{64}$ 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.

Topik & Kata Kunci

physics.comp-ph cond-mat.other math.NA quant-ph

Penulis (3)

Lev Barash

Stefan Güttel

Itay Hen

Format Sitasi

APA MLA BibTeX

Barash, L., Güttel, S., Hen, I. (2021). Calculating elements of matrix functions using divided differences. https://arxiv.org/abs/2107.14124

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Informasi Jurnal

Tahun Terbit: 2021
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓