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SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2018, Volume 39, Issue 1, pp. 426 - 450
Journal Article
SIAM Journal on Scientific Computing, ISSN 1064-8275, 2013, Volume 35, Issue 2, pp. B376 - B400
Journal Article
SIAM journal on scientific computing, ISSN 1095-7197, 2018, Volume 40, Issue 1, pp. A331 - A365
Journal Article
Journal of the Optical Society of America A: Optics and Image Science, and Vision, ISSN 1084-7529, 11/2015, Volume 32, Issue 11, pp. 2074 - 2081
When calculating the focusing properties of cylindrically symmetric focusing optics, numerical wave propagation calculations can be carried out using the quasi-discrete Hankel transform (QDHT... 
FIELDS | X-RAYS | FRESNEL ZONE PLATES | BEAM-PROPAGATION | DISCRETE HANKEL TRANSFORM | OPTICS | LANCZOS REDUCTION | LENSES | ARNOLDI METHOD | Utilities | Wave propagation | Mathematical analysis | Focusing | Transforms | X-rays | Symmetry | Fresnel zones
Journal Article
Journal of Computational Physics, ISSN 0021-9991, 09/2016, Volume 321, pp. 1120 - 1143
Journal Article
Journal of computational physics, ISSN 0021-9991, 2007, Volume 221, Issue 1, pp. 148 - 157
... Schrödinger equations using the imaginary time propagation (ITP) method is described. Convergence properties and accuracy of 2nd and 4th order operator-splitting methods for the ITP method are studied using numerical examples... 
Operator-splitting | Imaginary time propagation | Schrödinger equation | Lanczos method | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Schrodinger equation | operator-splitting | PHYSICS, MATHEMATICAL | SUPERFLUID HE-4 | imaginary time propagation
Journal Article
SIAM journal on numerical analysis, ISSN 1095-7170, 2018, Volume 56, Issue 3, pp. 1547 - 1569
.... At the same time, and unlike most competing methods, we simplify integrals instead of discretizing them via quadrature at the outset-this gives us the flexibility to handle a variety of potentials, being particularly effective in the case of highly oscillatory potentials, where this strategy allows us to consider significantly larger time steps. 
Lanczos iterations | Oscillatory potentials | Simplified commutators | Anticommutators | Large time steps | Time-dependent potential | Lie algebra | Schrödinger equation | Integral-preserving | Magnus expansion | anticommutators | MATHEMATICS, APPLIED | APPROXIMATION | oscillatory potentials | integral-preserving | large time steps | Schrodinger equation | simplified commutators | CONVERGENCE | time-dependent potential | INTEGRATORS | PROPAGATION
Journal Article
Computer physics communications, ISSN 0010-4655, 2015, Volume 188, pp. 189 - 197
Journal Article
by Wu, YM and Lou, X and Jin, YQ and Hou, ZG and Xiao, LZ and Zou, N and Zhou, HJ and Liu, Y
Communications in computational physics, ISSN 1815-2406, 08/2020, Volume 28, Issue 2, pp. 661 - 678
In this work, the full vectorial beam propagation methods (BPMs) are adopted for the calculations of the electromagnetic wave propagation from the two dimensional and three dimensional optical waveguide structures... 
BEAM | FIELDS | Wave propagation | STABILITY | fast solver | PADE APPROXIMANT | PHYSICS, MATHEMATICAL | Lanczos method | perfectly matched layer
Journal Article
Journal of Computational Science, ISSN 1877-7503, 2011, Volume 2, Issue 2, pp. 178 - 187
.... ► We compare the proposed method with traditional duality -based error estimates. We use a posteriori error estimation theory to derive a relation between local and global error in the propagation for the time-dependent... 
h, p-adaptivity | Time-dependent Schrödinger equation | Magnus–Lanczos propagator | Global error control | Magnus-Lanczos propagator | H, p-adaptivity | MAGNUS INTEGRATORS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTER SCIENCE, THEORY & METHODS | Time-dependent Schrodinger equation | ELECTRONIC STATES
Journal Article
Journal of Chemical Physics, ISSN 0021-9606, 03/2009, Volume 130, Issue 9, pp. 094101 - 094101-8
... and to extract from them information about potential energy surfaces. These methods enable one to disentangle the spectrum of a molecule to determine, for example... 
ROTATION | STATES | POLYATOMIC-MOLECULES | Coriolis force | rotational-vibrational states | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | REACTIVE SCATTERING | MECHANICAL CALCULATIONS | LANCZOS CALCULATION | vibrational states | VECTOR PARAMETRIZATION | organic compounds | VIBRATIONAL-ENERGY LEVELS | SPECTRA | PROPAGATION
Journal Article
Computer Physics Communications, ISSN 0010-4655, 2011, Volume 182, Issue 4, pp. 935 - 939
.... Introduction of a finite temporal basis reduces the problem to a set of linear equations, while an appropriate choice of temporal basis set offers improved convergence relative to methods based... 
Time dependence | Action | Time dependent Schrödinger equation | Propagator | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EVOLUTION | LANCZOS | PHYSICS, MATHEMATICAL | Time dependent Schrodinger equation | DEPENDENT SCHRODINGER-EQUATION | Wave propagation | Mathematical analysis | Evolution | Wavefunctions | Linear equations | Temporal logic | Convergence
Journal Article
JOURNAL OF CHEMICAL PHYSICS, ISSN 0021-9606, 08/2011, Volume 135, Issue 6, p. 064101
In this paper we propose and test a method for computing numerically exact vibrational energy levels of a molecule with six atoms... 
FINITE BASIS REPRESENTATION | VARIATIONAL METHOD | POLYATOMIC-MOLECULES | LANCZOS PROPAGATION METHOD | TRIATOMIC-MOLECULES | DISCRETE VARIABLE REPRESENTATION | ALGORITHM | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | FORCE-FIELD | QUANTUM DYNAMICS CALCULATIONS | 4-ATOM MOLECULES
Journal Article
Electronic Transactions on Numerical Analysis, ISSN 1068-9613, 2007, Volume 28, pp. 114 - 135
This paper presents a reformulation of Krylov Subspace Spectral (KSS) Methods, which build on Gene Golub's many contributions pertaining to moments and Gaussian... 
Wave equation | Stability | Heat equation | Variable-coefficient | Gaussian quadrature | Lanczos method | Spectral methods | MATHEMATICS, APPLIED | spectral methods | PSEUDO-DIFFERENTIAL OPERATORS | heat equation | wave equation | QUADRATURE | EQUATIONS | variable-coefficient | stability | WAVE-PROPAGATION
Journal Article
The Journal of Chemical Physics, ISSN 0021-9606, 05/2020, Volume 152, Issue 20, p. 204311
We report the vibrational energy levels of vinyl radical (VR) that are computed with a Lanczos eigensolver and a contracted basis. Many of the levels of the... 
QUANTUM DYNAMICS | STATES | LANCZOS PROPAGATION METHOD | SPECTROSCOPY | MATRICES | ALGORITHM | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | ENERGY-LEVELS | REPRESENTATION | CHEMISTRY, PHYSICAL | EIGENSOLVERS | MOLECULES | Potential energy | Red shift | Energy levels | Computation | Mathematical analysis | Vinyl radical | Wave functions | Doppler effect
Journal Article
The Journal of Physical Chemistry A, ISSN 1089-5639, 09/2018, Volume 122, Issue 38, pp. 7540 - 7547
Many mode-specific behaviors in the gas phase and at the gas-surface interface have been reported in the past decades. Infrared activation of a reagent... 
ORGANIC-SYNTHESIS | LANCZOS PROPAGATION METHOD | SPECTROSCOPY | HYDROPEROXYL | POTENTIAL-ENERGY SURFACES | MODE | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | DYNAMICS | CHEMISTRY, PHYSICAL | HO2 | SPECTRA | UNIMOLECULAR REACTIONS
Journal Article
Journal of Chemical Physics, ISSN 0021-9606, 03/2013, Volume 138, Issue 10, p. 104106
Journal Article
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