Gregory Beylkin

Papers and Preprints

                                                                                              | 2021 | 2020 |
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         1999 | 1998 | 1997 | 1996 | 1995 | 1994 | 1993 | 1992 | 1991 | 1990 |
         1989 | 1988 | 1987 | 1986 | 1985 | 1984 | 1983 | 1982-... |


G. Beylkin, S. Sharma, A fast algorithm for computing the Boys function, The Journal of Chemical Physics, 155, 174117, (2021)

S. Sharma, G. Beylkin, Efficient Evaluation of Two-Center Gaussian Integrals in Periodic Systems, J. Chem. Theory Comput. , 17, 7, 3916–3922 (2021)

J. Anderson, R.J. Harrison, B. Sundahl, W.S. Thornton, G. Beylkin, Real-space quasi-relativistic quantum chemistry, Computational and Theoretical Chemistry, 1175, 112711, (2020)


J. Anderson, B. Sundahl, R.J. Harrison, G. Beylkin, Dirac-Fock calculations on molecules in an adaptive multiwavelet basis, The Journal of Chemical Physics, 151, 234112, (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, (2019)

M.S. Mitchell, M.T. Miecnikowski, G. Beylkin, S.E.Parker, Efficient Fourier Basis Particle Simulation, Journal of Computational Physics, 396, (2019) 837–847,

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, (2019)

G. Beylkin,  L. Monzon and X. Yang , Reduction of multivariate mixtures and its applications, Journal of Computational Physics, 383, (2019) 94–124,


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,

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,



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),

M. Reynolds, G. Beylkin and A. Doostan , Optimization via separated representations and the canonical tensor decomposition, Journal of Computational Physics , 348, (2017) 220–230,


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,

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,

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,


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),

D. J. Biagioni, D. Beylkin and G. Beylkin, Randomized interpolative decomposition of separated representations,  Journal of Computational Physics , 281, (2015) 116–134


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



R. D. Lewis, G. Beylkin and L. Monzón,  Fast and accurate propagation of coherent light,    online supplementProceedings 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



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



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



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 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, 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


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 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, Approximations and Fast Algorithms, Proceedings of SPIE, v. 4478, 2001



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


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. 


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 


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


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 


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 


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


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.


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


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.