Papers and Preprints
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2019
J. Anderson, R.J. Harrison, H. Sekino, B. Sundahl,
G. Beylkin, G.I. Fann, S.R. Jensen, I. Sagert,
On derivatives of smooth functions represented
in multiwavelet bases, Journal of Computational Physics X, 4, 100033, https://doi.org/10.1016/j.jcpx.2019.100033
M.S. Mitchell, M.T. Miecnikowski, G. Beylkin, S.E.Parker,
Efficient Fourier Basis Particle Simulation, Journal of Computational Physics, 396, (2019) 837–847, https://doi.org/10.1016/j.jcp.2019.07.023
G. Beylkin, L. Monzon and X. Yang
,
Adaptive algorithm for electronic structure calculations using reduction of Gaussian
mixtures, Proceedings of the Royal Society A, 475: 2226, 20180901, https://dx.doi.org/10.1098/rspa.2018.0901
G. Beylkin, L. Monzon and X. Yang
,
Reduction of multivariate mixtures and its applications, Journal of Computational Physics, 383, (2019) 94–124, https://dx.doi.org/10.1016/j.jcp.2019.01.015
2018
S.L. Castro, L.A. Monzon, G.A. Wick, R.D. Lewis, G. Beylkin ,
Subpixel variability and quality assessment of satellite sea surface temperature data using a novel High Resolution Multistage Spectral Interpolation (HRMSI) technique,
Remote Sensing of Environment, 217, (2018), 292–308, https://dx.doi.org/10.1016/j.rse.2018.08.019
G. Beylkin, L. Monzon and I. Satkauskas
,
On computing distributions of products of non-negative independent random variables,
Applied and Computational Harmonic Analysis, 46, (2019), 400--416,
http://dx.doi.org/10.1016/j.acha.2018.01.002
2017
G. Beylkin, L. Monzon and I. Satkauskas
,
On computing distributions of products of random variables via Gaussian multiresolution analysis, Applied and Computational Harmonic Analysis, 47, 306--337,
(2017), http://dx.doi.org/10.1016/j.acha.2017.08.008
M. Reynolds, G. Beylkin and A. Doostan , Optimization via separated representations and the canonical tensor decomposition, Journal of Computational Physics , 348, (2017) 220–230, http://dx.doi.org/10.1016/j.jcp.2017.07.012
2016
M. Reynolds, A. Doostan and G. Beylkin, Randomized alternating least squares for canonical tensor decompositions: application to a PDE with random data, SIAM J. Sci. Comput., 38, 5,
(2016), A2634–A2664, http://dx.doi.org/10.1137/15M1042802
G. Beylkin and L. Monzon,
Efficient representation and accurate evaluation of oscillatory
integrals and functions, Discrete and Continuous Dynamical Systems, 36,
8, (2016) 4077–4100, http://dx.doi.org/10.3934/dcds.2016.36.4077
R.J. Harrison, G. Beylkin, F.A. Bischoff, J.A. Calvin, G.I.
Fann, J. Fosso-Tande, D. Galindo, J.R. Hammond, R. Hartman-Baker, J.C.
Hill, J. Jia, J.S. Kottmann, M.J Ou, L.E. Ratcliff, M.G. Reuter, A.C.
Richie-Halford, N.A. Romero, H. Sekino, W.A. Shelton, B.E. Sundahl,
W.S. Thornton, E.F. Valeev, Á. Vázquez-Mayagoitia, N. Vence, Y. Yokoi , MADNESS: A Multiresolution, Adaptive Numerical Environment for Scientific Simulation, SIAM J. Sci. Comput., 38,
(5) (2016) S123–S142, http://dx.doi.org/10.1137/15M1026171
2015
T. Yanai, G.I. Fann, G. Beylkin and R.J. Harrison, Multiresolution quantum
chemistry in multiwavelet bases: excited states from time-dependent
Hartree–Fock and density
functional theory via linear response,
Phys. Chem. Chem. Phys,
(2015), http://dx.doi.org/10.1039/c4cp05821f
D. J. Biagioni, D. Beylkin and G. Beylkin,
Randomized interpolative decomposition of separated representations,
Journal of Computational
Physics
, 281, (2015) 116–134
2014
B.K. Bradley, B.A. Jones, G. Beylkin,
K. Sandberg and P. Axelrad,
Bandlimited
implicit Runge–Kutta
integration for Astrodynamics,
119, (2014) 143–168
G. Beylkin and K. Sandberg, ODE solvers
using band-limited approximations,
Journal of Computational
Physics
, 265, (2014) 156–171
2013
R. D. Lewis, G. Beylkin and L. Monzón, Fast and accurate propagation of coherent
light,
online supplement, Proceedings of the Royal Society A, 469,
(2013) 20130323
G. Beylkin and T.S. Haut, Nonlinear
approximations for electronic structure calculations,
Proceedings of the Royal Society A, 469,
(2013) 20130231
A. Damle, G. Beylkin, T.S. Haut and L. Monzon, Near optimal rational approximations of
large data sets,
Applied and
Computational Harmonic
Analysis, 35, (2013) 251--263
M. Reynolds, G. Beylkin and L. Monzon, On generalized Gaussian quadratures for
bandlimited exponentials,
Applied and
Computational Harmonic
Analysis, 34, (2013) 352--365
M. Reynolds, G. Beylkin and L. Monzon, Rational approximations for tomographic
reconstructions,
Inverse Problems, 29,
6, (2013) 065020
T.S. Haut, G. Beylkin and L. Monzon, Solving Burgers’ equation using optimal
rational approximations,
Applied and
Computational Harmonic
Analysis, 34, (2013) 83--95
2012
T. Haut and G. Beylkin, Fast
and
accurate con-eigenvalue algorithm for optimal rational approximations, SIAM J. Matrix Anal. Appl., 33, 4,
(2012) 1101--1125
G. Beylkin, R.D. Lewis and L. Monzon, On
the Design of Highly Accurate and Efficient IIR and FIR Filters, IEEE Trans. Signal Processing, 60,
8, (2012) 4045--4054
G. Beylkin, G. Fann, R.J. Harrison, C. Kurcz and L. Monzon, Multiresolution representation of
operators
with boundary conditions on simple domains, Applied and Computational Harmonic
Analysis, 33, (2012) 109--139
2011
B. A. Jones, G. Beylkin, G. H. Born and R.S. Provence, A multiresolution model for small-body
gravity
estimation, Celest. Mech.
Dyn. Astr, 111, (2011) 309--335
2010
G. Beylkin and L. Monzon, Approximation
by exponential sums revisited,
Applied and
Computational Harmonic
Analysis, 28, (2010) 131--149
B. A. Jones, G. H. Born and G. Beylkin, Comparisons
of the cubed-sphere gravity model with the spherical harmonics, Journal of guidance, control, and
dynamics, 33, 2, (2010) 415--425
2009
B. A. Jones, G. H. Born and G. Beylkin, A
cubed sphere gravity model for fast orbit propagation, in AAS/AIAA Spaceflight Mechanics Meeting,
Advances in the Astronautical Sciences, 134, (2009) 567-584
K. Sandberg and G. Beylkin, Full-wave-equation
depth extrapolation for migration , Geophysics, 74, (2009)
WCA121-WCA128
C. Ahrens and G. Beylkin, Rotationally
invariant quadratures for the sphere,
Proceedings of the Royal Society A, 465,
(2009) 3103--3125
G. Beylkin and L. Monzon, Nonlinear
inversion of a bandlimited Fourier transform, Applied and Computational Harmonic
Analysis, 27, (2009) 351--366
G. Beylkin, C. Kurcz and L. Monzon, Fast
convolution with the free space Helmholtz Green's function, Journal of Computational Physics
, 228, (8) (2009) 2770–2791
G. Beylkin, J. Garcke and M. J. Mohlenkamp, Multivariate Regression and Machine Learning
with Sums of Separable Functions, SIAM J. Sci. Comput., 31,
(3) (2009) 1840-1857
2008
G. Beylkin, C. Kurcz and L. Monzon, Fast
algorithms for Helmholtz Green's functions,
Proceedings of the Royal Society A,
464, (2008) 3301--3326
G. Beylkin, M. J. Mohlenkamp and F. Perez, Approximating
a Wavefunction as an
Unconstrained
Sum of Slater Determinants,
Journal of Mathematical Physics, 49, (2008)
G. Beylkin, V. Cheruvu and F. Perez, Fast
adaptive algorithms in the
non-standard form for multidimensional problems, Applied and Computational Harmonic
Analysis, 24 (2008) 354--377
2007
G. Beylkin, M. J. Mohlenkamp and F. Perez, Preliminary
results on approximating a wavefunction as an unconstrained sum of
Slater determinants, Proc. Appl.
Math. Mech., 7, (2007)
G. Beylkin, C. Kurcz and L. Monzon, Grids
and transforms for band-limited
functions in a disk,
Inverse Problems, 23,
(2007) 2059-2088
G. Beylkin, R. Cramer, G. Fann and R. J. Harrison, Multiresolution separated representations of
singular and weakly singular operators, Applied and Computational Harmonic
Analysis, 23, (2007) 235-253
2006
L. Genovese, T. Deutsch, A. Neelov, S. Goedecker, and G.
Beylkin,
Efficient solution of Poisson's equation
with free boundary conditions, J.
Chem. Phys., 125
(7) (2006)
2005
G. Beylkin and M. J. Mohlenkamp, Algorithms
for numerical analysis in high
dimensions,
SIAM J. Sci. Comput.,
26
(6) (2005) 2133-2159
F. Andersson and G. Beylkin, The fast
Gauss
transform with complex
parameters,
J. Comput. Phys. 203 (2005)
274-286.
G. Beylkin and K. Sandberg, Wave
propagation using bases for bandlimited
functions,
Wave Motion 41 (3) (2005)
263-291
G. Beylkin and L. Monzon, On
approximation
of functions by exponential
sums,
Applied and Computational Harmonic
Analysis, 19 (2005) 17-48
2004
T. Yanai, G. Fann, Z. Gan, R. Harrison and G.
Beylkin, Multiresolution
quantum chemistry:
Hartree-Fock exchange,
J. Chem. Phys. 121 (14) (2004)
6680-6688.
T. Yanai, G. Fann, Z. Gan, R. Harrison and G. Beylkin, Multiresolution quantum chemistry:
Analytic
derivatives for Hartree-Fock and density functional theory, J. Chem. Phys. 121 (7) (2004)
2866-2876.
G. Fann, G. Beylkin, R. Harrison and K. Jordan,
Singular
operators in multiwavelet bases
IBM Journal of Research and
Development 48 (2) (2004) 161-171.
R. Harrison, G. Fann, T. Yanai, Z. Gan and G. Beylkin, Multiresolution quantum chemistry: basic
theory
and initial applications, J.
Chem. Phys. 121 (23) (2004)
11587-11598.
2003
R. Harrison, G. Fann, T. Yanai and G. Beylkin, Multiresolution quantum chemistry in
multiwavelet bases
in: P.M.A. Sloot et. al. (Ed.), Lecture Notes in Computer
Science. Computational
Science-ICCS 2003,
Vol. 2660, Springer, 2003, pp. 103-110.
K. Sandberg, D. Mastronarde and G. Beylkin, A
fast reconstruction algorithm for
electron
microscope tomography
Journal of Structural Biology 144 (2003) 61-72
2002
G. Beylkin and M. J. Mohlenkamp, Numerical
operator calculus in higher dimensions,
Proceedings of the National
Academy of Sciences, v.
99,
16, pp. 10246-10251, 2002
G. Beylkin and L. Monzon, On
generalized Gaussian quadratures for exponentials and their applications,
Applied and Computational Harmonic Analysis, v. 12,
pp. 332-373, 2002
K.Willam, I.Rhee and G. Beylkin, Multiresolution
Analysis of Elastic
Degradation in Heterogeneous Materials,
Meccanica 36, pp. 131-150, 2001
G. Beylkin and R. Cramer, Toward
Multiresolution Estimation and Efficient Representation of
Gravitational Fields,
Celestial Mechanics and Dynamical Astronomy, v. 84, 1, pp.
87-104,
2002
G. Beylkin and R. Cramer, A
Multiresolution Approach to Regularization of Singular Operators and
Fast Summation,
SIAM Journal on Scientific Computing, v.24, 1, pp. 81-117, 2002
B. Alpert, G. Beylkin, D. Gines, and L. Vozovoi, Adaptive
Solution of Partial Differential Equations in Multiwavelet Bases,
Journal of Computational Physics, v. 182, pp. 149-190,
2002
2001
G. Beylkin, Approximations
and Fast
Algorithms, Proceedings of SPIE, v. 4478, 2001
1999
G.Beylkin, N.Coult and M.J.Mohlenkamp, Fast
Spectral Projection Algorithms for Density-Matrix Computations,
Journal of
Computational Physics, v. 152, pp. 32-54, 1999
L. Monzon, G.Beylkin and W.Hereman, Compactly
supported wavelets based on almost interpolating and nearly linear
phase
filters (coiflets),
Applied and Computational Harmonic Analysis, 7, pp.
184-210,
1999
1998
G. Beylkin, J.M. Keiser and L.Vozovoi, A new
class of time discretization
schemes for the solution of nonlinear
PDEs,
Journal of
Computational Physics, v. 147, pp. 362-387,
1998
Lecture notes for Mathematical Geophysics Summer School at
Stanford, August 1998
These notes are introductions into the applications of USFFT and the
transform coding
G. Beylkin, On
Applications of Unequally Spaced Fast Fourier Transforms
G. Beylkin and A.Vassiliou, Wavelet
transforms and compression of seismic data
G. Beylkin, On
Multiresolution Methods in Numerical Analysis
, Invited Lecture at ICM98,
Documenta Mathematica, Extra Volume ICM 1998, III, pp. 481-490,
1998
G. Beylkin, M. Brewster and A. Gilbert, A
Multiresolution Strategy for Numerical Homogenization of Nonlinear ODEs,
Applied and Computational Harmonic Analysis, 5, pp.
450-486,
1998
G.Beylkin and N.Coult, A
Multiresolution strategy for reduction of elliptic PDE's and eigenvalue
problems,
Applied and Computational Harmonic Analysis, 5, pp.
129-155,
1998
D. L. Gines, G. Beylkin and J. Dunn, LU
Factorization of Non-Standard Forms and Direct Multiresolution Solvers,
Applied and Computational Harmonic Analysis, 5, pp. 156-201,
1998
A. Averbuch, G. Beylkin, R.R. Coifman, and M. Israeli, Multiscale Inversion of Elliptic
Operators,
in Signal and Image Representations in Combined Spaces, pp.
1-16, Volume 7 in the Wavelet Analysis and Applications series,
Academic
Press.
1997
G. Beylkin and J. M. Keiser, An
Adaptive Pseudo-Wavelet Approach for Solving Nonlinear Partial
Differential
Equations
Chapter in Multiscale Wavelet Methods for Partial Differential
Equations,,
Volume 6 in the Wavelet Analysis and Applications series, Academic
Press.
G. Beylkin and J. M. Keiser, On the
Adaptive Numerical Solution of
Nonlinear Partial Differential Equations in Wavelet Bases, Journal of Computational
Physics, vol. 132, pp. 233-259,
1997
1996
G. Beylkin and B. Torresani, Implementation
of operators via filter banks, autocorrelation shell and Hardy wavelets,
Applied and Computational Harmonic Analysis, 3, pp. 164-185,
1996
1995
M. E. Brewster and G. Beylkin, A
Multiresolution strategy for numerical homogenization,
Applied and Computational Harmonic Analysis, 2, pp.327-349
1995
G. Beylkin, On
the Fast Fourier Transform of Functions With Singularities,
Applied and Computational Harmonic Analysis, 2, pp. 363-381,
1995
G. Beylkin, On
factored FIR approximation of IIR filters,
Applied and Computational Harmonic Analysis, 2, pp. 293-298,
1995
1994
G. Beylkin, Fast
and accurate computation of the Fourier transform of an image,
Proceedings of SPIE, vol. 2277, pp. 244-252, 1994
G. Beylkin, On
wavelet-based algorithms for solving differential equations
Chapter in the book Wavelets: Mathematics and Applications,
CRC Press, 1994
1993
G. Beylkin, Wavelets
and Fast Numerical Algorithms,
Lecture Notes for short course, AMS-93,
Proceedings of Symposia in Applied Mathematics, v.47, pp.
89-117,
1993
N. Saito and G. Beylkin, Multiresolution
Representations using the Auto-Correlation Functions of Compactly
Supported
Wavelets,
Schlumberger-Doll Research Tech. Rep., 1991, IEEE Transactions on Signal
Processing, v. 41, 12, pp.3584-3590,
1993.
G. Beylkin,
On
the fast algorithm for multiplication of functions in the wavelet bases
In Proceedings of the International Conference "Wavelets and
Applications",
Toulouse, 1992, Y. Meyer and S. Roques, edt., Editions Frontieres, 1993
B. Alpert, G. Beylkin, R.Coifman and V. Rokhlin, Wavelet-like bases for the fast solution
of
second-kind integral equations
SIAM Journal on Scientific Computing, 14, 1, pp.159-184,
January
1993
1992
G. Beylkin and N. Saito, Wavelets,
their autocorrelation functions, and multiresolution representation of
signals,
Expanded abstract in Proceedings ICASSP-92, v. 4, pp. 381-384,
1992
G. Beylkin, On
the representation of operators in bases of compactly supported wavelets
SIAM Journal on Numerical Analysis, 29, 6, pp.1716-1740,
December
1992
G. Beylkin, R. Coifman and V. Rokhlin, Wavelets in numerical analysis
in: Wavelets and their applications, Jones and Bartlett, Boston, MA,
1992, pp. 181-210.
1991
G. Beylkin, Wavelets,
Multiresolution Analysis and Fast Numerical Algorithms, A draft of
INRIA lectures, May 1991
G. Beylkin, R. Coifman and V. Rokhlin, Fast Wavelet Transforms and Numerical
Algorithms
I.
Comm. Pure Appl. Math. 44 (2) (1991) 141-183.
1990
G. Beylkin and R. Burridge, Linearized
inverse scattering problems in acoustics and elasticity
Wave Motion, 12, 1, pp. 15-52, 1990
1989
M. Cheney, G. Beylkin, E. Somersalo and R. Burridge, Three-dimensional
inverse scattering for the wave equation with variable speed: near
field
formulae using point sources
Inverse Problems, 5, pp. 1-6, 1989
1988
R. Burridge and G. Beylkin, On
double integrals over spheres
Inverse Problems, 4, pp. 1-10, 1988
1987
W. Chang, P. Carrion and G. Beylkin, Wavefront
sets of solutions to linearised inverse scattering problems
Inverse Problems, 3, 4, pp. 683-690, 1987
D. Miller, M. Oristaglio and G. Beylkin, A
new slant on seismic imaging: Migration and Integral geometry
Geophysics, 52, 7, pp. 943-964, July 1987
G. Beylkin, Discrete
Radon Transform
IEEE Trans. Acoustics Speech and Signal Processing, 35, 2, pp. 162-172,
1987
1986
G. Beylkin, A
mathematical theory for
reconstructing discontinuities in linearized inverse problems of wave
propagation
(expanded
abstract) in Mathematical and computational methods in seismic
exploration and reservoir modeling, SIAM, Philadelphia, PA, 1986
G. Beylkin, Mathematical
theory for
seismic migration and spatial resolution
in Deconvolution and Inversion, EAEG/SEG, Blackwell Scientific
Publications, pp. 291-305, 1986
1985
G. Beylkin and M. Oristaglio, Distorted-wave
Born and distorted-wave Rytov approximations
Optics Communications, 53, 4, pp. 213-216, 1985
G. Beylkin, Reconstructing
discontinuities in multidimensional inverse scattering problems: smooth
errors versus small errors
Applied Optics, 24, 23, pp. 4086-4088, 1985
G. Beylkin, M. Oristaglio and
D. Miller, Spatial
resolution of
migration algorithms
in A.J.Berkhout, J.Ridder, van der Waal L.F. (Eds.), Acoustical
Imaging, 14, Plenum Pub. Co., pp. 155-167, 1985
G. Beylkin, Imaging
of discontinuities in the inverse scattering problem by inversion of a
causal generalized Radon transform
Journal of Mathematical Physics, 26, 1, pp. 99-108, January 1985
1984
A.J. Devaney and G. Beylkin, Diffraction
Tomography using arbitrary transmitter and receiver surfaces
Ultrasonic Imaging, 6, pp. 181-193, 1984
G. Beylkin, The inversion
problem and
applications of the generalized Radon transform
Communications on Pure and Applied Mathematics, Vol. XXXVII, pp.
579-599, 1984
1983
G. Beylkin, Iterated
Spherical Means in
Linearized Inversze Problems
in Conference on Inverse Scattering: Theory and Applications, SIAM,
Philadelphia, 1983
G. Beylkin, The
fundamental identity
for
iterated spherical means and the inversion formula for diffraction
tomography and inverse scattering
Journal of Mathematical Physics, 24, 6, pp. 1399-1400, June 1983
1982-...
G. Beylkin, Stability and
uniqueness of
the solution of the inverse kinematic problem of seismology in higher
dimensions,
Journal of Soviet Mathematics, v. 21, 3, pp. 251-254,
Translation of Zapiski Nauchnykh Seminarov LOMI (Notes of Scientific
Seminars of V.A. Steklov Mathematical Institute, Leningrad
Branch) v. 84, 1979.