<div class="csl-bib-body">
<div class="csl-entry">Jawecki, T. (2022, August 2). <i>A practical approach on rational approximations to the action of unitary matrix exponentials</i> [Conference Presentation]. computational mathematics for quantum technologies, Workshop, United Kingdom of Great Britain and Northern Ireland (the).</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/146116
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dc.description.abstract
Approximations to the action of unitary matrix exponentials provide numerical methods for time propagation of spatially discretized linear Schrödinger-type equations. The discretized problem, besides resolving frequencies which are relevant for the given initial state, often includes perturbations in relatively high frequency ranges. Such perturbations can critically affect the convergence of (polynomial) approximations to the action of the matrix exponential. Our approach is to generate unitary rational approximants in barycentric rational form which are accurate in relevant frequency ranges. Due to unitarity, the effect of perturbations is negligible - a property which yields strong advantages in this setting. Relevant frequency ranges (relevant parts of the matrix spectrum) are detected on the run using estimates on the spectral distribution of the initial state. These estimates are based on the Lanczos method and bounds on quadrature weights of Gaussian quadrature formulae.
en
dc.language.iso
en
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dc.subject
unitary rational approximation
en
dc.subject
discretized Schrödinger equation
en
dc.title
A practical approach on rational approximations to the action of unitary matrix exponentials
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.rights.holder
Tobias Jawecki
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dc.type.category
Conference Presentation
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tuw.publication.invited
invited
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tuw.researchTopic.id
Q3
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tuw.researchTopic.id
C4
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tuw.researchTopic.name
Quantum Modeling and Simulation
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tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.value
30
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tuw.researchTopic.value
70
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tuw.publication.orgunit
E136 - Institut für Theoretische Physik
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tuw.event.name
computational mathematics for quantum technologies