Papers and Preprints
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2024
G. Beylkin, On representations of the Helmholtz Green's function,听Applied and Computational Harmonic Analysis, 70, 101633, (2024),听
2022
S. Sharma, A.F. White, G. Beylkin,听Fast Exchange with Gaussian Basis Set Using Robust Pseudospectral Method, Journal of Chemical Theory and Computation, 18, (12) , 7306-7320, (2022)
2021
G. Beylkin, S. Sharma,听A fast algorithm for computing the Boys function, The Journal of Chemical Physics,听155, 174117, (2021)
S. Sharma, G. Beylkin,听Efficient Evaluation of Two-Center Gaussian Integrals in Periodic Systems, J. Chem. Theory Comput. ,听17, 7, 3916鈥�3922 (2021)
2020
J. Anderson, R.J. Harrison, B. Sundahl, W.S. Thornton, G. Beylkin,听Real-space quasi-relativistic quantum chemistry, Computational and Theoretical Chemistry,听1175, 112711, (2020)
2019
J. Anderson, B. Sundahl, R.J. Harrison, G. Beylkin,听Dirac-Fock calculations on molecules in an adaptive multiwavelet basis, The Journal of Chemical Physics,听151, 234112, (2019)
J. Anderson, R.J. Harrison, H. Sekino, B. Sundahl, G. Beylkin, G.I. Fann, S.R. Jensen, I. Sagert,听On derivatives of smooth functions represented in multiwavelet bases, Journal of Computational Physics X,听4, 100033, (2019)
M.S. Mitchell, M.T. Miecnikowski, G. Beylkin, S.E.Parker,听Efficient Fourier Basis Particle Simulation, Journal of Computational Physics,听396, (2019) 837鈥�847,
G. Beylkin,听 L. Monzon and X. Yang听,听Adaptive algorithm for electronic structure calculations using reduction of Gaussian mixtures, Proceedings of the Royal Society A,听475: 2226, 20180901, (2019)
G. Beylkin,听 L. Monzon and X. Yang听,听Reduction of multivariate mixtures and its applications, Journal of Computational Physics,听383, (2019) 94鈥�124,
2018
S.L. Castro,听 L.A. Monzon, G.A. Wick, R.D. Lewis, G. Beylkin听,听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鈥�308,
G. Beylkin,听 L. Monzon and I. Satkauskas听,听On computing distributions of products of non-negative independent random variables,听Applied and Computational Harmonic Analysis,听46, (2019), 400--416,听
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2017
G. Beylkin,听 L. Monzon and I. Satkauskas听,听On computing distributions of products of random variables via Gaussian multiresolution analysis, Applied and Computational Harmonic Analysis,听47, 306--337,听(2017),听
M. Reynolds,听G. Beylkin and A. Doostan听,听Optimization via separated representations and the canonical tensor decomposition,听Journal of Computational Physics听,听348, (2017) 220鈥�230,
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2016
M. Reynolds,听 A. Doostan and G. Beylkin,听Randomized alternating least squares for canonical tensor decompositions: application to a PDE with random data,听SIAM J. Sci. Comput., 38, 5,听(2016), A2634鈥揂2664,
G. Beylkin and L. Monzon,听Efficient representation and accurate evaluation of oscillatory integrals and functions, Discrete and Continuous Dynamical Systems, 36, 8, 听 (2016) 4077鈥�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, 脕. V谩zquez-Mayagoitia, N. Vence, Y. Yokoi听,听MADNESS: A Multiresolution, Adaptive Numerical Environment for Scientific Simulation,听SIAM J.听 Sci. Comput.,听38, (5) (2016) S123鈥揝142,
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2015
T. Yanai, G.I. Fann, G. Beylkin and R.J. Harrison,听,听听Phys. Chem. Chem. Phys,听(2015),
D. J. Biagioni, D. Beylkin and G. Beylkin,听Randomized interpolative decomposition of separated representations,听听Journal of Computational Physics听,听281, (2015) 116鈥�134
听
2014
B.K. Bradley, B.A. Jones, G. Beylkin, K. Sandberg and P. Axelrad, 听听Bandlimited implicit Runge鈥揔utta integration for Astrodynamics,听听听119, (2014) 143鈥�168
G. Beylkin and K. Sandberg,听ODE solvers using band-limited approximations,听听Journal of Computational Physics听,听265, (2014) 156鈥�171
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2013
R. D. Lewis, G. Beylkin and L. Monz贸n,听听Fast and accurate propagation of coherent light,听听听听online supplement,听
G. Beylkin and T.S. Haut,听Nonlinear approximations for electronic structure calculations,听听听
A. Damle,听 G. Beylkin, T.S. Haut and L. Monzon,听听Near optimal rational approximations of large data sets,听听听听Applied and Computational Harmonic Analysis,听35, (2013) 251--263
M. Reynolds,听 G. Beylkin and L. Monzon,听听On generalized Gaussian quadratures for bandlimited exponentials,听听听听Applied and Computational Harmonic Analysis,听34, (2013) 352--365
M. Reynolds,听 G. Beylkin and L. Monzon,听听Rational approximations for tomographic reconstructions,听听听 Inverse Problems,听29, 6, (2013) 065020
T.S. Haut, G. Beylkin and L. Monzon,听听Solving Burgers鈥� equation using optimal rational approximations,听听听听Applied and Computational Harmonic Analysis,听34, (2013) 83--95
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2012
T. Haut and G. Beylkin, 听听Fast and accurate con-eigenvalue algorithm for optimal rational approximations,听听听SIAM J. Matrix Anal. Appl.,听33, 4, (2012) 1101--1125
G. Beylkin, R.D. Lewis and L. Monzon,听听On the Design of Highly Accurate and Efficient IIR and FIR Filters,听听听IEEE Trans. Signal Processing,听60, 8, (2012) 4045--4054
G. Beylkin, G. Fann, R.J. Harrison, C. Kurcz and L. Monzon,听Multiresolution representation of operators with boundary conditions on simple domains,听听Applied and Computational Harmonic Analysis,听33, (2012) 109--139
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2011
B. A. Jones, G. Beylkin, G. H. Born and R.S. Provence,听A multiresolution model for small-body gravity estimation,听听 Celest. Mech. Dyn. Astr,听111,听 (2011) 309--335
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2010
G. Beylkin and L. Monzon,听Approximation by exponential sums revisited,听听Applied and Computational Harmonic Analysis,听28, (2010) 131--149
B. A. Jones, G. H. Born and G. Beylkin,听Comparisons of the cubed-sphere gravity model with the spherical harmonics,听听 Journal of guidance, control, and dynamics,听33, 2, (2010) 415--425
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2009
B. A. Jones, G. H. Born and G. Beylkin,听A cubed sphere gravity model for fast orbit propagation,听听in AAS/AIAA Spaceflight Mechanics Meeting, Advances in the Astronautical Sciences,听134, (2009) 567-584
K. Sandberg and G. Beylkin,听Full-wave-equation depth extrapolation for migration听,听Geophysics,听74, (2009) WCA121-WCA128
C. Ahrens and G. Beylkin,听Rotationally invariant quadratures for the sphere,听听听
G. Beylkin and L. Monzon,听Nonlinear inversion of a bandlimited Fourier transform,听听Applied and Computational Harmonic Analysis,听27, (2009)听351--366
G. Beylkin, C. Kurcz and L. Monzon,听Fast convolution with the free space Helmholtz Green's function,听听Journal of Computational Physics ,听听228, (8) (2009) 2770鈥�2791
G. Beylkin, J. Garcke and M. J. Mohlenkamp,听Multivariate Regression and Machine Learning with Sums of Separable Functions,听听SIAM J.听 Sci. Comput.,听31, (3) (2009) 1840-1857
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2008
G. Beylkin, C. Kurcz and L. Monzon,听Fast algorithms for Helmholtz Green's functions,听听听
G. Beylkin, M. J. Mohlenkamp and F. Perez,听Approximating a Wavefunction as an Unconstrained Sum of Slater Determinants,听听Journal of Mathematical Physics,听听49, (2008)听
G. Beylkin, V. Cheruvu and F. Perez,听Fast adaptive algorithms in the non-standard form for multidimensional problems,听听Applied and Computational Harmonic Analysis,听24 (2008)听354--377
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2007
G. Beylkin, M. J. Mohlenkamp and F. Perez,听Preliminary results on approximating a wavefunction as an unconstrained sum of Slater determinants, Proc. Appl. Math. Mech.,听听7, 听(2007)听
G. Beylkin, C. Kurcz and L. Monzon,听Grids and transforms for band-limited functions in a disk,
Inverse Problems,听 23, (2007) 2059-2088
G. Beylkin, R. Cramer, G. Fann and R. J. Harrison,听Multiresolution separated representations of singular and weakly singular operators, Applied and Computational Harmonic Analysis,听 23, (2007) 235-253
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2006
L. Genovese, T. Deutsch, A. Neelov, S. Goedecker, and G. Beylkin,听Efficient solution of Poisson's equation with free boundary conditions,听J. Chem. Phys.,听 125 (7) (2006)
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2005
G. Beylkin and M. J. Mohlenkamp,听Algorithms for numerical analysis in high dimensions,
SIAM听 J. Sci. Comput.,听 26 (6) (2005) 2133-2159
F. Andersson and G. Beylkin,听The fast Gauss transform with complex parameters,
J. Comput. Phys. 203 (2005) 274-286.
G. Beylkin and K. Sandberg,听听Wave propagation using bases for bandlimited functions,
Wave Motion听41 (3) (2005) 263-291
G. Beylkin and L. Monzon,听On approximation of functions by exponential sums,
Applied and Computational Harmonic Analysis, 19 (2005) 17-48
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2004
T. Yanai, G. Fann, Z. Gan, R. Harrison and听 G. Beylkin,听Multiresolution quantum chemistry: Hartree-Fock exchange,
J. Chem. Phys. 121 (14) (2004) 6680-6688.
T. Yanai, G. Fann, Z. Gan, R. Harrison and听 G. Beylkin,听Multiresolution quantum chemistry: Analytic derivatives for Hartree-Fock and density functional theory,听J. Chem. Phys. 121 (7) (2004) 2866-2876.
G. Fann, G. Beylkin, R. Harrison and K. Jordan,听Singular operators in multiwavelet bases
IBM Journal of Research and Development听48 (2) (2004) 161-171.
R. Harrison, G. Fann, T. Yanai, Z. Gan and G. Beylkin,听Multiresolution quantum chemistry: basic theory and initial applications,听听J. Chem. Phys. 121 (23) (2004) 11587-11598.
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2003
R. Harrison, G. Fann, T. Yanai and G. Beylkin,听Multiresolution quantum chemistry in multiwavelet bases
in: P.M.A. Sloot et. al. (Ed.), 听Lecture Notes in Computer Science.听听Computational Science-ICCS 2003, Vol. 2660, Springer, 2003, pp. 103-110.
K. Sandberg, D. Mastronarde and G. Beylkin,听A fast reconstruction algorithm for electron microscope tomography
Journal of Structural Biology 144 (2003) 61-72
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2002
G. Beylkin and M. J. Mohlenkamp,听Numerical operator calculus in higher dimensions,
Proceedings of the National Academy of Sciences,听 v. 99,听 16, pp. 10246-10251, 2002
G. Beylkin and L. Monzon,听On generalized Gaussian quadratures for exponentials and their applications,
Applied and Computational Harmonic Analysis,听 v. 12,听 pp. 332-373, 2002
K.Willam, I.Rhee and G. Beylkin,听Multiresolution Analysis of Elastic Degradation in Heterogeneous Materials,
Meccanica听36, pp. 131-150, 2001
G. Beylkin听 and听 R. Cramer,听Toward Multiresolution Estimation and Efficient Representation of Gravitational Fields,
Celestial Mechanics and Dynamical Astronomy, v. 84, 1, pp. 87-104, 2002
G. Beylkin听 and听 R. Cramer,听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,听 and听 L. Vozovoi,听Adaptive Solution of Partial Differential Equations in Multiwavelet Bases,听听Journal of Computational Physics,听 v. 182, pp. 149-190, 2002
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2001
G. Beylkin,听Approximations and Fast Algorithms, Proceedings of SPIE, v. 4478, 2001
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1999
G.Beylkin, N.Coult and M.J.Mohlenkamp,听Fast Spectral Projection Algorithms for Density-Matrix Computations,
听Journal of Computational Physics,听 v. 152, pp. 32-54, 1999
L. Monzon, G.Beylkin and W.Hereman,听Compactly supported wavelets based on almost interpolating and nearly linear phase filters (coiflets),听Applied and Computational Harmonic Analysis,听 7, pp. 184-210, 1999
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1998
G. Beylkin, J.M. Keiser and L.Vozovoi,听A new class of time discretization schemes for the solution of nonlinear PDEs,
听Journal of Computational Physics,听 v. 147, pp. 362-387, 1998听
Lecture notes for听Mathematical Geophysics Summer School听at Stanford, August 1998
These notes are introductions into the applications of USFFT and the transform coding
G. Beylkin,听On Applications of Unequally Spaced Fast Fourier Transforms
G. Beylkin and A.Vassiliou,听Wavelet transforms and compression of seismic data
G. Beylkin,听On Multiresolution Methods in Numerical Analysis听, Invited Lecture at ICM98,
Documenta Mathematica, Extra Volume ICM 1998, III, pp. 481-490, 1998听
G. Beylkin, M. Brewster and A. Gilbert,听A Multiresolution Strategy for Numerical Homogenization of Nonlinear ODEs,
Applied and Computational Harmonic Analysis,听 5, pp. 450-486, 1998
G.Beylkin and N.Coult,听A Multiresolution strategy for reduction of elliptic PDE's and eigenvalue problems,
Applied and Computational Harmonic Analysis, 5,听 pp. 129-155, 1998听
D. L. Gines, G. Beylkin and J. Dunn,听LU Factorization of Non-Standard Forms and Direct Multiresolution Solvers,
Applied and Computational Harmonic Analysis, 5, pp. 156-201, 1998听
A. Averbuch, G. Beylkin, R.R. Coifman, and M. Israeli,听Multiscale Inversion of Elliptic Operators,
in听Signal and Image Representations in Combined Spaces,听pp. 1-16, Volume 7 in the Wavelet Analysis and Applications series, Academic Press.听
听
1997
G. Beylkin and J. M. Keiser,听An Adaptive Pseudo-Wavelet Approach for Solving Nonlinear Partial Differential Equations
Chapter in听Multiscale Wavelet Methods for Partial Differential Equations,, Volume 6 in the Wavelet Analysis and Applications series, Academic Press.听
G. Beylkin and J. M. Keiser,听On the Adaptive Numerical Solution of Nonlinear Partial Differential Equations in Wavelet Bases,听听Journal of Computational Physics, vol. 132, pp. 233-259, 1997听
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1996
G. Beylkin and B. Torresani,听Implementation of operators via filter banks, autocorrelation shell and Hardy wavelets,
Applied and Computational Harmonic Analysis, 3, pp. 164-185, 1996
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1995
M. E. Brewster and G. Beylkin,听A Multiresolution strategy for numerical homogenization,
Applied and Computational Harmonic Analysis, 2, pp.327-349 1995听
G. Beylkin,听On the Fast Fourier Transform of Functions With Singularities,
Applied and Computational Harmonic Analysis, 2, pp. 363-381, 1995听
G. Beylkin,听On factored FIR approximation of IIR filters,
Applied and Computational Harmonic Analysis, 2, pp. 293-298, 1995听
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1994
G. Beylkin,听Fast and accurate computation of the Fourier transform of an image,
Proceedings of SPIE, vol. 2277, pp. 244-252, 1994
G. Beylkin,听On wavelet-based algorithms for solving differential equations
Chapter in the book听听Wavelets: Mathematics and Applications, CRC Press, 1994听
听
1993
G. Beylkin,听Wavelets and Fast Numerical Algorithms,
Lecture Notes for short course, AMS-93,听Proceedings of Symposia in Applied Mathematics, v.47, pp. 89-117, 1993听
N. Saito and G. Beylkin,听Multiresolution Representations using the Auto-Correlation Functions of Compactly Supported Wavelets,
Schlumberger-Doll Research Tech. Rep., 1991,听IEEE Transactions on Signal Processing, v. 41, 12, pp.3584-3590, 1993.听
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,听Wavelet-like bases for the fast solution of second-kind integral equations
SIAM Journal on Scientific Computing, 14, 1, pp.159-184, 听January 1993
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1992
G. Beylkin and N. Saito,听Wavelets, their autocorrelation functions, and multiresolution representation of signals,
Expanded abstract in听Proceedings ICASSP-92, v. 4, pp. 381-384, 1992听
G. Beylkin,听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听 V. Rokhlin,听Wavelets in numerical analysis
in: Wavelets and their applications, Jones and Bartlett, Boston, MA, 1992, pp. 181-210.
听
1991
G. Beylkin,听Wavelets, Multiresolution Analysis and Fast Numerical Algorithms, A draft of INRIA lectures, May 1991
G. Beylkin, R. Coifman and听 V. Rokhlin,听Fast Wavelet Transforms and Numerical Algorithms I.
Comm. Pure Appl. Math. 44 (2) (1991) 141-183.
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1990
G. Beylkin and R. Burridge,听Linearized inverse scattering problems in acoustics and elasticity
Wave Motion, 12, 1, pp. 15-52, 1990
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1989
M. Cheney, G. Beylkin, E. Somersalo and R. Burridge,听Three-dimensional inverse scattering for the wave equation with variable speed: near field formulae using point sources
Inverse Problems, 5, pp. 1-6, 1989
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1988
R. Burridge and G. Beylkin,听On double integrals over spheres
Inverse Problems, 4, pp. 1-10, 1988
听
1987
W. Chang, P. Carrion and G. Beylkin,听Wavefront sets of solutions to linearised inverse scattering problems
Inverse Problems, 3, 4, pp. 683-690, 1987
D. Miller, M. Oristaglio and G. Beylkin,听A new slant on seismic imaging: Migration and Integral geometry
Geophysics, 52, 7,听 pp. 943-964, July 1987
G. Beylkin,听Discrete Radon Transform
IEEE Trans. Acoustics Speech and Signal Processing, 35, 2, pp. 162-172, 1987
听
1986
G. Beylkin,听A mathematical theory for reconstructing discontinuities in linearized inverse problems of wave propagation
(expanded abstract) in听Mathematical and computational methods in seismic exploration and reservoir modeling, SIAM, Philadelphia, PA, 1986
G. Beylkin,听Mathematical theory for seismic migration and spatial resolution
in Deconvolution and Inversion, EAEG/SEG, Blackwell Scientific Publications, pp. 291-305, 1986
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1985
G. Beylkin and M. Oristaglio,听Distorted-wave Born and distorted-wave Rytov approximations
Optics Communications, 53, 4, pp. 213-216, 1985
G. Beylkin,听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,听听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,听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
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1984
A.J. Devaney and G. Beylkin,听Diffraction Tomography using arbitrary transmitter and receiver surfaces
Ultrasonic Imaging, 6, pp. 181-193, 1984
G. Beylkin,听The inversion problem and applications of the generalized Radon transform
Communications on Pure and Applied Mathematics, Vol. XXXVII, pp. 579-599, 1984
听
1983
G. Beylkin,听Iterated Spherical Means in Linearized Inversze Problems
in Conference on Inverse Scattering: Theory and Applications, SIAM, Philadelphia, 1983
G. Beylkin,听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
听
1982
G. Beylkin,听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, 听 Translation of Zapiski Nauchnykh Seminarov LOMI (Notes of Scientific Seminars of 听 V.A. Steklov Mathematical Institute, Leningrad Branch) v. 84, 1979.
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