Adapting the Lanczos algorithm to matrices with almost continuous spectra.

Vladimir Druskin

Jörn T. Zimmerling Vladimir Druskin Adapting the Lanczos algorithm to matrices with almost continuous spectra. 2026 February abs/2602.11449 CoRR https://doi.org/10.48550/arXiv.2602.11449 db/journals/corr/corr2602.html#abs-2602-11449 streams/journals/corr

Justin M. Baker Elena Cherkaev Vladimir Druskin Shari Moskow Mikhail Zaslavsky Regularized reduced order Lippmann-Schwinger-Lanczos method for inverse scattering problems in the frequency domain. 113725 2025 525 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2025.113725 db/journals/jcphy/jcphy525.html#BakerCDMZ25 streams/journals/jcphy

Jörn T. Zimmerling Vladimir Druskin Valeria Simoncini Monotonicity, Bounds and Acceleration of Block Gauss and Gauss-Radau Quadrature for Computing B<sup>T</sup> φ (A) B. 5 2025 April 103 J. Sci. Comput. 1 https://doi.org/10.1007/s10915-025-02799-z db/journals/jscic/jscic103.html#ZimmerlingDS25 streams/journals/jscic

Vladimir Druskin Jörn T. Zimmerling A Krylov projection algorithm for large symmetric matrices with dense spectra. 2025 April abs/2504.06998 CoRR https://doi.org/10.48550/arXiv.2504.06998 db/journals/corr/corr2504.html#abs-2504-06998 streams/journals/corr

Vladimir Druskin Shari Moskow Mikhail Zaslavsky On optimality and bounds for internal solutions generated from boundary data-driven Gramians. 2025 April abs/2504.15407 CoRR https://doi.org/10.48550/arXiv.2504.15407 db/journals/corr/corr2504.html#abs-2504-15407 streams/journals/corr

Jörn T. Zimmerling Mikhail Zaslavsky Alexander V. Mamonov Vladimir Druskin Anarzhan Abilgazy Lippmann-Schwinger-Lanczos algorithm for inverse scattering problems with unknown reflectivity and loss distributions: One-dimensional Case. 2025 November abs/2511.15058 CoRR https://doi.org/10.48550/arXiv.2511.15058 db/journals/corr/corr2511.html#abs-2511-15058 streams/journals/corr

Vladimir Druskin Shari Moskow Mikhail Zaslavsky Reduced Order Modeling Inversion of Monostatic Data in a Multi-scattering Environment. 334-350 2024 March 17 SIAM J. Imaging Sci. 1 https://doi.org/10.1137/23m1564365 db/journals/siamis/siamis17.html#DruskinMZ24

Vladimir Druskin Shari Moskow Mikhail Zaslavsky ROM Inversion of Monostatic Data Lifted to Full MIMO. 2196-2211 2024 17 SIAM J. Imaging Sci. 4 https://doi.org/10.1137/24m165778x db/journals/siamis/siamis17.html#DruskinMZ24a streams/journals/siamis

Vladimir Druskin Shari Moskow Mikhail Zaslavsky ROM inversion of monostatic data lifted to full MIMO. 2024 abs/2407.00822 CoRR https://doi.org/10.48550/arXiv.2407.00822 db/journals/corr/corr2407.html#abs-2407-00822 streams/journals/corr

Jörn T. Zimmerling Vladimir Druskin Valeria Simoncini Monotonicity, bounds and extrapolation of Block-Gauss and Gauss-Radau quadrature for computing B<sup>T</sup> φ (A) B. 2024 abs/2407.21505 CoRR https://doi.org/10.48550/arXiv.2407.21505 db/journals/corr/corr2407.html#abs-2407-21505 streams/journals/corr

Jörn T. Zimmerling Vladimir Druskin Murthy N. Guddati Elena Cherkaev Rob Remis Solving inverse scattering problems via reduced-order model embedding procedures. 2023 abs/2306.08465 CoRR https://doi.org/10.48550/arXiv.2306.08465 db/journals/corr/corr2306.html#abs-2306-08465

Justin M. Baker Elena Cherkaev Vladimir Druskin Shari Moskow Mikhail Zaslavsky Regularized Reduced Order Lippman-Schwinger-Lanczos Method for Inverse Scattering Problems in the Frequency Domain. 2023 abs/2311.16367 CoRR https://doi.org/10.48550/arXiv.2311.16367 db/journals/corr/corr2311.html#abs-2311-16367

Vladimir Druskin Alexander V. Mamonov Mikhail Zaslavsky Distance Preserving Model Order Reduction of Graph-Laplacians and Cluster Analysis. 32 2022 90 J. Sci. Comput. 1 https://doi.org/10.1007/s10915-021-01660-3 https://www.wikidata.org/entity/Q118126683 db/journals/jscic/jscic90.html#DruskinMZ22

Vladimir Druskin Stefan Güttel Leonid Knizhnerman Model order reduction of layered waveguides via rational Krylov fitting. 2022 abs/2203.17052 CoRR https://doi.org/10.48550/arXiv.2203.17052 db/journals/corr/corr2203.html#abs-2203-17052

Vladimir Druskin Shari Moskow Mikhail Zaslavsky Reduced order modeling inversion of mono static data in a multi-scattering environment. 2022 abs/2211.08319 CoRR https://doi.org/10.48550/arXiv.2211.08319 db/journals/corr/corr2211.html#abs-2211-08319

Liliana Borcea Vladimir Druskin Jörn T. Zimmerling A Reduced Order Model Approach to Inverse Scattering in Lossy Layered Media. 1 2021 89 J. Sci. Comput. 1 https://doi.org/10.1007/s10915-021-01616-7 db/journals/jscic/jscic89.html#BorceaDZ21

Vladimir Druskin Shari Moskow Mikhail Zaslavsky Lippmann-Schwinger-Lanczos algorithm for inverse scattering problems. 2021 abs/2101.12317 CoRR https://arxiv.org/abs/2101.12317 db/journals/corr/corr2101.html#abs-2101-12317

Vladimir Druskin Shari Moskow Mikhail Zaslavsky On extension of the data driven ROM inverse scattering framework to partially nonreciprocal arrays. 2021 abs/2112.09634 CoRR https://arxiv.org/abs/2112.09634 db/journals/corr/corr2112.html#abs-2112-09634

Liliana Borcea Vladimir Druskin Alexander V. Mamonov Mikhail Zaslavsky Jörn T. Zimmerling Reduced Order Model Approach to Inverse Scattering. 685-723 2020 13 SIAM J. Imaging Sci. 2 https://doi.org/10.1137/19M1296355 https://www.wikidata.org/entity/Q118126685 db/journals/siamis/siamis13.html#BorceaDMZZ20

Liliana Borcea Vladimir Druskin Jörn T. Zimmerling A reduced order model approach to inverse scattering in lossy layered media. 2020 abs/2012.00861 CoRR https://arxiv.org/abs/2012.00861 db/journals/corr/corr2012.html#abs-2012-00861

Liliana Borcea Vladimir Druskin Alexander V. Mamonov Mikhail Zaslavsky Robust nonlinear processing of active array data in inverse scattering via truncated reduced order models. 1-26 2019 381 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2018.12.021 https://www.wikidata.org/entity/Q118126686 db/journals/jcphy/jcphy381.html#BorceaDMZ19

Vladimir Druskin Mikhail Zaslavsky Fast finite-difference convolution for 3D problems in layered media. 2019 abs/1909.01299 CoRR http://arxiv.org/abs/1909.01299 db/journals/corr/corr1909.html#abs-1909-01299

Liliana Borcea Vladimir Druskin Alexander V. Mamonov Shari Moskow Mikhail Zaslavsky Reduced order models for spectral domain inversion: Embedding into the continuous problem and generation of internal data. 2019 abs/1909.06460 CoRR http://arxiv.org/abs/1909.06460 db/journals/corr/corr1909.html#abs-1909-06460

Liliana Borcea Vladimir Druskin Alexander V. Mamonov Mikhail Zaslavsky Jörn T. Zimmerling Reduced Order Model Approach to Inverse Scattering. 2019 abs/1910.13014 CoRR http://arxiv.org/abs/1910.13014 db/journals/corr/corr1910.html#abs-1910-13014

Vladimir Druskin Robert F. Remis Mikhail Zaslavsky Jörn T. Zimmerling Compressing Large-Scale Wave Propagation Models via Phase-Preconditioned Rational Krylov Subspaces. 1486-1518 2018 16 Multiscale Model. Simul. 4 https://doi.org/10.1137/17M1156848 db/journals/mmas/mmas16.html#DruskinRZZ18

Vladimir Druskin Alexander V. Mamonov Mikhail Zaslavsky A Nonlinear Method for Imaging with Acoustic Waves Via Reduced Order Model Backprojection. 164-196 2018 11 SIAM J. Imaging Sci. 1 https://doi.org/10.1137/17M1133580 https://www.wikidata.org/entity/Q118126689 db/journals/siamis/siamis11.html#DruskinMZ18

Vladimir Druskin Alexander V. Mamonov Mikhail Zaslavsky Clustering of graph vertex subset via Krylov subspace model reduction. 2018 abs/1809.03048 CoRR http://arxiv.org/abs/1809.03048 db/journals/corr/corr1809.html#abs-1809-03048

Vladimir Druskin Alexander V. Mamonov Mikhail Zaslavsky Multiscale S-Fraction Reduced-Order Models for Massive Wavefield Simulations. 445-475 2017 15 Multiscale Model. Simul. 1 https://doi.org/10.1137/16M1072103 https://www.wikidata.org/entity/Q118126691 db/journals/mmas/mmas15.html#DruskinMZ17

Murthy N. Guddati Vladimir Druskin Ali Vaziri Astaneh Exponential convergence through linear finite element discretization of stratified subdomains. 429-447 2016 322 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2016.06.045 https://www.wikidata.org/entity/Q57430343 db/journals/jcphy/jcphy322.html#GuddatiDA16

Vladimir Druskin Alexander V. Mamonov Andrew E. Thaler Mikhail Zaslavsky Direct, Nonlinear Inversion Algorithm for Hyperbolic Problems via Projection-Based Model Reduction. 684-747 2016 9 SIAM J. Imaging Sci. 2 https://doi.org/10.1137/15M1039432 https://www.wikidata.org/entity/Q118126694 db/journals/siamis/siamis9.html#DruskinMTZ16

Vladimir Druskin Stefan Güttel Leonid Knizhnerman Near-Optimal Perfectly Matched Layers for Indefinite Helmholtz Problems. 90-116 2016 58 SIAM Rev. 1 https://doi.org/10.1137/140966927 db/journals/siamrev/siamrev58.html#DruskinGK16

Vladimir Druskin Rob Remis Mikhail Zaslavsky An extended Krylov subspace model-order reduction technique to simulate wave propagation in unbounded domains. 608-618 2014 272 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2014.04.051 db/journals/jcphy/jcphy272.html#DruskinRZ14

Vladimir Druskin Valeria Simoncini Mikhail Zaslavsky Adaptive Tangential Interpolation in Rational Krylov Subspaces for MIMO Dynamical Systems. 476-498 2014 35 SIAM J. Matrix Anal. Appl. 2 https://doi.org/10.1137/120898784 db/journals/siammax/siammax35.html#DruskinSZ14

Vladimir Druskin Rob Remis A Krylov Stability-Corrected Coordinate-Stretching Method to Simulate Wave Propagation in Unbounded Domains. 2013 35 SIAM J. Sci. Comput. 2 https://doi.org/10.1137/12087356X db/journals/siamsc/siamsc35.html#DruskinR13

Vladimir Druskin Valeria Simoncini Mikhail Zaslavsky Solution of the Time-Domain Inverse Resistivity Problem in the Model Reduction Framework Part I. One-Dimensional Problem with SISO Data. 2013 35 SIAM J. Sci. Comput. 3 https://doi.org/10.1137/110852607 db/journals/siamsc/siamsc35.html#DruskinSZ13

Vladimir Druskin Valeria Simoncini Adaptive rational Krylov subspaces for large-scale dynamical systems. 546-560 2011 60 Syst. Control. Lett. 8 https://doi.org/10.1016/j.sysconle.2011.04.013 db/journals/scl/scl60.html#DruskinS11

Vladimir Druskin Leonid Knizhnerman Valeria Simoncini Analysis of the Rational Krylov Subspace and ADI Methods for Solving the Lyapunov Equation. 1875-1898 2011 49 SIAM J. Numer. Anal. 5 https://doi.org/10.1137/100813257 db/journals/siamnum/siamnum49.html#DruskinKS11

Mikhail Zaslavsky Vladimir Druskin Solution of time-convolutionary Maxwell's equations using parameter-dependent Krylov subspace reduction. 4831-4839 2010 229 J. Comput. Phys. 12 https://doi.org/10.1016/j.jcp.2010.03.019 db/journals/jcphy/jcphy229.html#ZaslavskyD10

Vladimir Druskin Chad Lieberman Mikhail Zaslavsky On Adaptive Choice of Shifts in Rational Krylov Subspace Reduction of Evolutionary Problems. 2485-2496 2010 32 SIAM J. Sci. Comput. 5 https://doi.org/10.1137/090774082 db/journals/siamsc/siamsc32.html#DruskinLZ10

Valeria Simoncini Vladimir Druskin Convergence Analysis of Projection Methods for the Numerical Solution of Large Lyapunov Equations. 828-843 2009 47 SIAM J. Numer. Anal. 2 https://doi.org/10.1137/070699378 db/journals/siamnum/siamnum47.html#SimonciniD09

Leonid Knizhnerman Vladimir Druskin Mikhail Zaslavsky On Optimal Convergence Rate of the Rational Krylov Subspace Reduction for Electromagnetic Problems in Unbounded Domains. 953-971 2009 47 SIAM J. Numer. Anal. 2 https://doi.org/10.1137/080715159 db/journals/siamnum/siamnum47.html#KnizhnermanDZ09

Vladimir Druskin Leonid Knizhnerman Mikhail Zaslavsky Solution of Large Scale Evolutionary Problems Using Rational Krylov Subspaces with Optimized Shifts. 3760-3780 2009 31 SIAM J. Sci. Comput. 5 https://doi.org/10.1137/080742403 db/journals/siamsc/siamsc31.html#DruskinKZ09

Aria Abubakar Tarek M. Habashy Vladimir Druskin Leonid Knizhnerman An enhanced Gauss-Newton inversion algorithm using a dual-optimal grid approach. 1419-1427 2006 44 IEEE Trans. Geosci. Remote. Sens. 6 https://doi.org/10.1109/TGRS.2006.872297 db/journals/tgrs/tgrs44.html#AbubakarHDK06

Sergey Asvadurov Vladimir Druskin Murthy N. Guddati Leonid Knizhnerman On Optimal Finite-Difference Approximation of PML. 287-305 2003 41 SIAM J. Numer. Anal. 1 https://doi.org/10.1137/S0036142901391451 db/journals/siamnum/siamnum41.html#AsvadurovDGK03

Vladimir Druskin Shari Moskow Three-point finite-difference schemes, Padé and the spectral Galerkin method. I. One-sided impedance approximation. 995-1019 2002 71 Math. Comput. 239 db/journals/moc/moc71.html#DruskinM02 https://doi.org/10.1090/S0025-5718-01-01349-7

Vladimir Druskin Leonid Knizhnerman Gaussian spectral rules for second order finite-difference schemes. 139-159 2000 25 Numer. Algorithms 1-4 https://doi.org/10.1023/A:1016600805438 db/journals/na/na25.html#DruskinK00

Vladimir Druskin Leonid Knizhnerman Gaussian Spectral Rules for the Three-Point Second Differences: I. A Two-Point Positive Definite Problem in a Semi-Infinite Domain. 403-422 1999 37 SIAM J. Numer. Anal. 2 https://doi.org/10.1137/S0036142997330792 db/journals/siamnum/siamnum37.html#DruskinK99

Vladimir Druskin On the Uniqueness of Inverse Problems from Incomplete Boundary Data. 1591-1603 1998 58 SIAM J. Appl. Math. 5 https://doi.org/10.1137/S0036139996298292 db/journals/siamam/siamam58.html#Druskin98

Vladimir Druskin Leonid Knizhnerman Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions. 755-771 1998 July 19 SIAM J. Matrix Anal. Appl. 3 https://doi.org/10.1137/s0895479895292400 db/journals/siammax/siammax19.html#DruskinK98

Vladimir Druskin Anne Greenbaum Leonid Knizhnerman Using Nonorthogonal Lanczos Vectors in the Computation of Matrix Functions. 38-54 1998 19 SIAM J. Sci. Comput. 1 https://doi.org/10.1137/S1064827596303661 db/journals/siamsc/siamsc19.html#DruskinGK98

Vladimir Druskin Leonid Knizhnerman Krylov subspace approximation of eigenpairs and matrix functions in exact and computer arithmetic. 205-217 1995 2 Numer. Linear Algebra Appl. 3 https://doi.org/10.1002/nla.1680020303 db/journals/nla/nla2.html#DruskinK95

Anarzhan Abilgazy Aria Abubakar Ali Vaziri Astaneh Sergey Asvadurov Justin M. Baker Liliana Borcea Elena Cherkaev Anne Greenbaum Murthy N. Guddati Stefan Güttel Tarek M. Habashy Leonid Knizhnerman Chad Lieberman Alexander V. Mamonov Shari Moskow Rob RemisRobert F. Remis Valeria Simoncini Andrew E. Thaler Mikhail Zaslavsky Jörn T. Zimmerling