Commit efd4c999 authored by Patrick Buchfink's avatar Patrick Buchfink
Browse files

Added references for symplectic algorithms.

parent 53f68410
......@@ -120,6 +120,18 @@
publisher={SIAM}
}
@article{BBH2019,
author = {Buchfink, Patrick and Bhatt, Ashish and Haasdonk, Bernard},
title = {Symplectic Model Order Reduction with Non-Orthonormal Bases},
journal = {Mathematical and Computational Applications},
year = {2019},
volume = {24},
number = {2},
issn = {2297--8747},
article-number = {43},
doi = {10.3390/mca24020043},
}
@article{BEOR14,
title={A numerically stable a posteriori error estimator for reduced basis approximations of elliptic equations},
author={Buhr, Andreas and Engwer, Christian and Ohlberger, Mario and Rave, Stephan},
......@@ -334,6 +346,17 @@
doi = {10.1109/31.1720}
}
@article{PM16,
author = {Peng, L. and Mohseni, K.},
title = {Symplectic Model Reduction of Hamiltonian Systems},
journal = {SIAM Journal on Scientific Computing},
year = {2016},
volume = {38},
number = {1},
pages = {A1--A27},
doi = {10.1137/140978922},
}
@phdthesis{RL95,
title={Analysis and implementation of an implicitly restarted Arnoldi iteration},
author={Lehoucq, Richard Bruno},
......@@ -364,6 +387,17 @@
publisher={IEEE}
}
@article{S11,
title={Symplectic Gram-Schmidt Algorithm with Re-Orthogonalization},
author={Al-Aidarous, Eman Salem},
journal={Journal of King Abdulaziz University: Science},
volume={23},
number={1},
pages={11--20},
year = {2011},
doi = {10.4197/Sci.23-1.2},
}
@article{TRLBK14,
author = {Tu, J. H. and Rowley, C. W. and Luchtenburg, D. M. and Brunton, S. L. and Kutz, J. N.},
title = {On Dynamic Mode Decomposition: Theory and Applications},
......
......@@ -236,6 +236,8 @@ class SymplecticBasis(BasicObject):
def psd_svd_like_decomp(U, modes, balance=True):
"""Generates a |SymplecticBasis| with the PSD SVD-like decompostion.
This is an implementation of Algorithm 1 in :cite:`BBH19`.
Parameters
----------
U
......@@ -287,6 +289,8 @@ def psd_svd_like_decomp(U, modes, balance=True):
def psd_cotengent_lift(U, modes):
"""Generates a |SymplecticBasis| with the PSD cotangent lift.
This is an implementation of Algorithm 1 in :cite:`PM16`.
Parameters
----------
U
......@@ -316,6 +320,8 @@ def psd_cotengent_lift(U, modes):
def psd_complex_svd(U, modes):
"""Generates a |SymplecticBasis| with the PSD complex SVD.
This is an implementation of Algorithm 2 in :cite:`PM16`.
Parameters
----------
U
......@@ -347,10 +353,7 @@ def symplectic_gram_schmidt(E, F, return_Lambda=False, atol=1e-13, rtol=1e-13, o
lmax=2, check=True, check_tol=1e-3, copy=True):
"""Symplectify a |VectorArray| using the modified symplectic Gram-Schmidt algorithm.
Reference::
Salam (2005), On theoretical and numerical aspects of symplectic Gram--Schmidt-like
algorithms
This is an implementation of Algorithm 3.2. in :cite:`S11`.
Decomposition::
......
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