Papers and Preprints
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
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 algorithms for Helmholtz Green's functions, Proceedings of the Royal Society A, 464, (2008) 3301--3326
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
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
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
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)
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
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.
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
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, Approximations and Fast Algorithms, Proceedings of SPIE, v. 4478, 2001
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
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
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
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
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
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
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.
M. E. Brewster and G. Beylkin, A
Multiresolution strategy for numerical homogenization,
Applied and Computational Harmonic Analysis, 2, pp.327-349
1995
G. Beylkin, Fast
and accurate computation of the Fourier transform of an image,
Proceedings of SPIE, vol. 2277, pp. 244-252, 1994
Gregory Beylkin, On
the Fast Fourier Transform of Functions With Singularities,
Applied and Computational Harmonic Analysis, 2, pp. 363-381,
1995
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
G. Beylkin, On
factored FIR approximation of IIR filters,
Applied and Computational Harmonic Analysis, 2, pp. 293-298,
1995
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, 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
wavelet-based algorithms for solving differential equations
APPM preprint 153, Dec. 1992, Chapter in the book Wavelets: Mathematics and Applications,
CRC Press, 1994
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
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.
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.
G. Beylkin and
R. Burridge, Linearized inverse scattering problems in acoustics and elasticity
Wave Motion, 12, 1, pp. 15-52, 1990
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
R. Burridge and G. Beylkin, On
double integrals over spheres
Inverse Problems, 4, pp. 1-10, 1988
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
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
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
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
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