Numerical Methods for Large Eigenvalue Problems: Revised Edition

The Restarted Arnoldi Method Applied to Iterative Linear System Solvers for the Computation of Rightmost Eigenvalues

Meerbergen, K., & Roose, D. (1997) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479894274255 · Cited by 28

Some theoretical comparisons of refined Ritz vectors and Ritz vectors

Jia, Z. (2004) · Science in China Series A Mathematics · doi:10.1360/04za0020 · Cited by 28

A general method for implementing vibrationally adiabatic mixed quantum-classical simulations

Thompson, W. H. (2003) · The Journal of Chemical Physics · doi:10.1063/1.1528891 · Cited by 28

Computational Modeling and Least‐Squares Fittingof EPR Spectra

Stoll, S. (2014) · doi:10.1002/9783527672431.ch3 · Cited by 29

Conflict-free symmetric sparse matrix-vector multiplication on multicore architectures

Elafrou, A., Goumas, G., & Koziris, N. (2019) · 2012 International Conference for High Performance Computing, Networking, Storage and Analysis · doi:10.1145/3295500.3356148 · Cited by 27

RIEMANNIAN MANIFOLD TRUST-REGION METHODS WITH APPLICATIONS TO EIGENPROBLEMS

Baker, C. G. (2008) · Cited by 27

Preconditioned Krylov Subspace Methods for the Numerical Solution of Markov Chains

Saad, Y. E.-M. (1995) · Springer eBooks · doi:10.1007/978-1-4615-2241-6_4 · Cited by 27

A block variant of the GMRES method on massively parallel processors

Li, G. (1997) · Parallel Computing · doi:10.1016/s0167-8191(97)00004-5 · Cited by 27

Comparison study of electron correlation in one-photon and two-photon double ionization of helium

Jiang, W., Peng, L.-Y., Xiong, W.-H., et al. (2013) · Physical Review A · doi:10.1103/physreva.88.023410 · Cited by 27

An Arnoldi-Inout algorithm for computing PageRank problems

Gu, C., & Wang, W. (2016) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2016.05.026 · Cited by 27

Computing charge densities with partially reorthogonalized Lanczos

Bekas, C., Saad, Y. E.-M., Tiago, M. L., et al. (2005) · Computer Physics Communications · doi:10.1016/j.cpc.2005.05.005 · Cited by 27

A new look at pencils of matrix valued functions

Kunkel, P., & Mehrmann, V. (1994) · Linear Algebra and its Applications · doi:10.1016/0024-3795(94)90403-0 · Cited by 27

Bernstein spectral method for quasinormal modes and other eigenvalue problems

Fortuna, S., & Vega, I. (2023) · The European Physical Journal C · doi:10.1140/epjc/s10052-023-12350-9 · Cited by 26

Bound-State Calculations for Three Atoms Without Explicit Partial Wave Decomposition

Roudnev, V., Yakovlev, S. L., & Sofianos, S. A. (2005) · Few-Body Systems · doi:10.1007/s00601-005-0114-2 · Cited by 26

Inverse Iteration for Purely Imaginary Eigenvalues with Application to the Detection of Hopf Bifurcations in Large-Scale Problems

Meerbergen, K., & Spence, A. (2010) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/080742890 · Cited by 26

Inner iterations in the shift-invert residual Arnoldi method and the Jacobi-Davidson method

Jia, Z., & Li, C. (2014) · Science China Mathematics · doi:10.1007/s11425-014-4791-5 · Cited by 26

A numerical method for determining monotonicity and convergence rate in iterative learning control

Barton, K. L., Bristow, D. A., & Alleyne, A. G. (2009) · International Journal of Control · doi:10.1080/00207170903131177 · Cited by 26

Transition to complex dynamics in the cubic lid-driven cavity

López, J. M., Welfert, B. D., Wu, K., et al. (2017) · Physical Review Fluids · doi:10.1103/physrevfluids.2.074401 · Cited by 26

Harmonic and refined Rayleigh–Ritz for the polynomial eigenvalue problem

Hochstenbach, M. E., & Sleijpen, G. L. G. (2007) · Numerical Linear Algebra with Applications · doi:10.1002/nla.562 · Cited by 26

On adaptively accelerated Arnoldi method for computing PageRank

Yin, J., Yin, G., & Ng, M. K. (2011) · Numerical Linear Algebra with Applications · doi:10.1002/nla.789 · Cited by 26

ALGEBRAIC PROPERTIES OF THE BLOCK GMRES AND BLOCK ARNOLDI METHODS

Elbouyahyaoui, L., Messaoudi, A., & Sadok, H. (2009) · Cited by 26

Feasibility and competitiveness of a reduced basis approach for rapid electronic structure calculations in quantum chemistry

Cancès, É., Bris, C. L., Maday, Y., et al. (2007) · CRM proceedings & lecture notes · doi:10.1090/crmp/041/02 · Cited by 26

Subspace estimation and decomposition for hybrid analog-digital millimetre-wave MIMO systems

Ghauch, H., Bengtsson, M., Kim, T., et al. (2015) · IEEE International Workshop on Signal Processing Advances in Wireless Communications (SPAWC) · doi:10.1109/spawc.2015.7227067 · Cited by 25

Consistent pCMFD Acceleration Schemes of the Three-Dimensional Transport Code PROTEUS-MOC

Zhang, G., Hsieh, A., Yang, W. S., et al. (2019) · Nuclear Science and Engineering · doi:10.1080/00295639.2018.1560854 · Cited by 25

Modal analysis for nanoplasmonics with nonlocal material properties

Binkowski, F., Zschiedrich, L., Hammerschmidt, M., et al. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.100.155406 · Cited by 25

Arnoldi Method for Large Quaternion Right Eigenvalue Problem

Wang, Q., & Wang, X. (2020) · Journal of Scientific Computing · doi:10.1007/s10915-020-01158-4 · Cited by 24

Diagonalization of the Hamiltonian for finite-sized dispersive media: Canonical quantization with numerical mode decomposition

Na, D.-Y., Zhu, J., & Chew, W. C. (2021) · Physical Review A · doi:10.1103/physreva.103.063707 · Cited by 27

Linear and nonlinear sensor placement strategies for mean-flow reconstruction via data assimilation

Mons, V., & Marquet, O. (2021) · Journal of Fluid Mechanics · doi:10.1017/jfm.2021.488 · Cited by 24

Discovering Interpretable Directions in the Semantic Latent Space of Diffusion Models

Haas, R., Huberman-Spiegelglas, I., Mulayoff, R., Graßhof, S., Brandt, S. S., & Michaeli, T. (2024) · International Conference on Automatic Face and Gesture Recognition · doi:10.1109/fg59268.2024.10581912 · Cited by 45

A neutral stability curve for incompressible flows in a rectangular driven cavity

Abouhamza, A., & Pierre, R. (2003) · Mathematical and Computer Modelling · doi:10.1016/s0895-7177(03)90012-4 · Cited by 25

Anderson localization in high temperature QCD: background configuration properties and Dirac eigenmodes

Cossu, G., & Hashimoto, S. (2016) · Journal of High Energy Physics · doi:10.1007/jhep06(2016)056 · Cited by 25

Electro-vortex flow simulation using coupled meshes

Weber, N., Beckstein, P., Galindo, V., et al. (2018) · Computers & Fluids · doi:10.1016/j.compfluid.2018.03.047 · Cited by 25

Numerical Solution of Time-Dependent Problems with Fractional Power Elliptic Operator

Vabishchevich, P. N. (2017) · Computational Methods in Applied Mathematics · doi:10.1515/cmam-2017-0028 · Cited by 24

Complex frequency band structure of periodic thermo-diffusive materials by Floquet–Bloch theory

Bacigalupo, A., Bellis, M. L. D., & Gnecco, G. (2019) · Acta Mechanica · doi:10.1007/s00707-019-02416-9 · Cited by 25

A modified block Newton iteration for approximating an invariant subspace of a symmetric matrix

Lösche, R., Schwetlick, H., & Timmermann, G. (1998) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(97)10018-0 · Cited by 25

Sequential Computation of Transfer Function Dominant Poles of s-Domain System Models

Martins, N., Portela, C., & Junior, S. G. (2009) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2008.2012179 · Cited by 25

On the Spectrum of an Operator Pencil with Applications to Wave Propagation in Periodic and Frequency Dependent Materials

Engström, C., & Richter, M. (2009) · SIAM Journal on Applied Mathematics · doi:10.1137/080728779 · Cited by 25

Scalable Log Determinants for Gaussian Process Kernel LearningPreprint

Dong, K., Eriksson, D., Nickisch, H., Bindel, D., & Wilson, A. G. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1711.03481 · Cited by 61

Deep Learning Solution of the Eigenvalue Problem for Differential Operators

Ben-Shaul, I., Bar, L., Fishelov, D., & Sochen, N. (2023) · Neural Computation · doi:10.1162/neco_a_01583 · Cited by 24

Steady-state ab initio laser theory for fully or nearly degenerate cavity modes

Burkhardt, S., Liertzer, M., Krimer, D. O., et al. (2015) · Physical Review A · doi:10.1103/physreva.92.013847 · Cited by 24

Continuation of Bifurcations of Periodic Orbits for Large-Scale Systems

Net, M., & Sánchez, J. (2015) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/140981010 · Cited by 24

Sparso

Rong, H., Park, J., Xiang, L., et al. (2016) · International Conference on Parallel Architectures and Compilation Techniques · doi:10.1145/2967938.2967943 · Cited by 24

MU‐MIMO Downlink Capacity Analysis and Optimum Code Weight Vector Design for 5G Big Data Massive Antenna Millimeter Wave Communication

Abdo, A. M. A., Zhao, X., Zhang, R., et al. (2018) · Wireless Communications and Mobile Computing · doi:10.1155/2018/7138232 · Cited by 24

A model order reduction technique for systems with nonlinear frequency dependent damping

Jith, J., & Sarkar, S. (2019) · Applied Mathematical Modelling · doi:10.1016/j.apm.2019.08.030 · Cited by 24

Bifurcation scenario for a two-dimensional static airfoil exhibiting trailing edge stall

Busquet, D., Marquet, O., Richez, F., et al. (2021) · Journal of Fluid Mechanics · doi:10.1017/jfm.2021.767 · Cited by 24

Nearly reducible finite Markov chains: Theory and algorithms

Sharpe, D., & Wales, D. J. (2021) · The Journal of Chemical Physics · doi:10.1063/5.0060978 · Cited by 27

GMRES algorithms over 35 years

Zou, Q. (2023) · Applied Mathematics and Computation · doi:10.1016/j.amc.2023.127869 · Cited by 24

Acoustic Insulation Characteristics and Optimal Design of Membrane-Type Metamaterials Loaded with Asymmetric Mass Blocks

Jiang, R., Shi, G., Huang, C., et al. (2023) · Materials · doi:10.3390/ma16031308 · Cited by 24

A hybrid geometric + algebraic multigrid method with semi‐iterative smoothers

Lu, C., Jiao, X., & Missirlis, N. M. (2014) · Numerical Linear Algebra with Applications · doi:10.1002/nla.1925 · Cited by 26

A timestepper approach for the systematic bifurcation and stability analysis of polymer extrusion dynamics

Kavousanakis, M. E., Russo, L., Siettos, C. I., et al. (2007) · Journal of Non-Newtonian Fluid Mechanics · doi:10.1016/j.jnnfm.2007.11.002 · Cited by 24

Rayleigh–Bénard instability in a vertical cylinder with a rotating magnetic field

Walker, J. S., Volz, M. P., & Mazuruk, K. (2003) · International Journal of Heat and Mass Transfer · doi:10.1016/j.ijheatmasstransfer.2003.10.005 · Cited by 24

Subspace iteration techniques for the calculation of resonances using complex symmetric Hamiltonians

Sommerfeld, T., & Tarantelli, F. (2000) · The Journal of Chemical Physics · doi:10.1063/1.480778 · Cited by 24

On the Convergence of Rational Ritz Values

Beckermann, B., Güttel, S., & Vandebril, R. (2010) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/090755412 · Cited by 24

Error bounds of Rayleigh–Ritz type contour integral-based eigensolver for solving generalized eigenvalue problems

Imakura, A., Du, L., & Sakurai, T. (2015) · Numerical Algorithms · doi:10.1007/s11075-015-9987-4 · Cited by 24

Improving the Performance of the Symmetric Sparse Matrix-Vector Multiplication in Multicore

Gkountouvas, T., Karakasis, V., Kourtis, K., et al. (2013) · Proceedings - IEEE International Parallel and Distributed Processing Symposium · doi:10.1109/ipdps.2013.43 · Cited by 24

Optical properties of a semispherical quantum dot placed at the center of a cubic quantum box: Optical rectification, second and third-harmonic generations

Mohammadi, S. A., Khordad, R., & Rezaei, G. (2015) · Physica E Low-dimensional Systems and Nanostructures · doi:10.1016/j.physe.2015.10.016 · Cited by 24

Bifurcation analysis of the primary instability in the flow around a flexibly mounted circular cylinder

Dolci, D. I., & Carmo, B. (2019) · Journal of Fluid Mechanics · doi:10.1017/jfm.2019.754 · Cited by 24

Elastodiffusion and cluster mobilities using kinetic Monte Carlo simulations: Fast first-passage algorithms for reversible diffusion processes

Athènes, M., Kaur, S., Adjanor, G., et al. (2019) · Physical Review Materials · doi:10.1103/physrevmaterials.3.103802 · Cited by 24

Assessment of AC network modeling impact on small-signal stability of AC systems with VSC HVDC converters

Grdenić, G., Delimar, M., & Beerten, J. (2020) · International Journal of Electrical Power & Energy Systems · doi:10.1016/j.ijepes.2020.105897 · Cited by 24

A variant of the Power–Arnoldi algorithm for computing PageRank

Hu, Q.-Y., Wen, C., Huang, T., et al. (2020) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2020.113034 · Cited by 24

Anderson localization in high temperature QCD: background configuration properties and Dirac eigenmodes

Cossu, G., & Hashimoto, S. (2016) · Institutional Repositories DataBase (IRDB) · Cited by 24

A sub-linear scaling algorithm for computing the electronic structure of materials

Weinan, E., Garcı́a-Cervera, C. J., & Lu, J. (2007) · Communications in Mathematical Sciences · doi:10.4310/cms.2007.v5.n4.a14 · Cited by 24

A Rayleigh–Ritz preconditioner for the iterative solution to large scale nonlinear problems

Rey, C., & Risler, F. (1998) · Numerical Algorithms · doi:10.1023/a:1016680306741 · Cited by 24

Implicitly restarted arnoldi/lanczos methods and large scale svd applications

Sorensen, D. C. (1995) · Elsevier eBooks · doi:10.1016/b978-044482107-2/50003-0 · Cited by 24

Quasi-exact optical analysis of oxide-apertured microcavity VCSELs using vector finite elements

Noble, M. J., Lott, J. A., & Loehr, J. P. (1998) · IEEE Journal of Quantum Electronics · doi:10.1109/3.736102 · Cited by 24

“Direct” Calculation of Thermal Rate Constants for the F + H2 → HF + F Reaction

Wang, H., Thompson, W. H., & Miller, W. H. (1998) · The Journal of Physical Chemistry A · doi:10.1021/jp981461y · Cited by 24

Computing multi-eigenpairs of high-dimensional eigenvalue problems using tensor neural networks

Wang, Y., & Xie, H. (2024) · Journal of Computational Physics · doi:10.1016/j.jcp.2024.112928 · Cited by 23

A theoretical study of the rovibrational levels of the bosonic van der Waals neon trimer

Salci, M., Levin, S. B., Elander, N., et al. (2008) · The Journal of Chemical Physics · doi:10.1063/1.2955736 · Cited by 23

Optimized purification for density matrix calculation

Suryanarayana, P. (2012) · Chemical Physics Letters · doi:10.1016/j.cplett.2012.10.090 · Cited by 23

Diamagnetic susceptibility of an off-center hydrogenic donor in pyramid-like and cone-like quantum dots

Avazzadeh, Z., Bahramiyan, H., Khordad, R., et al. (2016) · The European Physical Journal Plus · doi:10.1140/epjp/i2016-16121-8 · Cited by 23

Indiscernible topological variations in DAE networks

Patil, D. U., Tesi, P., & Trenn, S. (2019) · Automatica · doi:10.1016/j.automatica.2018.12.012 · Cited by 23

Quadratic optimization with orthogonality constraints: explicit Łojasiewicz exponent and linear convergence of line-search methods

Liu, H., Wu, W., & So, A. M. (2016) · International Conference on Machine Learning · Cited by 23

The power method and beyond

Bai, Z., Wu, W.-T., & Muratova, G. V. (2020) · Applied Numerical Mathematics · doi:10.1016/j.apnum.2020.03.021 · Cited by 23

Vertical Federated Knowledge Transfer via Representation Distillation for Healthcare Collaboration Networks

Huang, C., Wang, L., & Han, X. G. (2023) · International World Wide Web Conference (WWW) · doi:10.1145/3543507.3583874 · Cited by 25

A specific reduction method for the branch modal formulation: Application to a highly non-linear configuration

Quéméner, O., Neveu, A., & Videcoq, É. (2006) · International Journal of Thermal Sciences · doi:10.1016/j.ijthermalsci.2006.11.011 · Cited by 23

An analysis of international data encryption algorithm(IDEA) security against differential cryptanalysis

Chen, J., Xue, D., & Lai, X. (2008) · Wuhan University Journal of Natural Sciences · doi:10.1007/s11859-008-0612-4 · Cited by 23

On the computation of a truncated SVD of a large linear discrete ill-posed problem

Onunwor, E., & Reichel, L. (2017) · Numerical Algorithms · doi:10.1007/s11075-016-0259-8 · Cited by 23

Multi-View Classification via a Fast and Effective Multi-View Nearest-Subspace Classifier

Shu, T., Zhang, B., & Tang, Y. Y. (2019) · IEEE Access · doi:10.1109/access.2019.2910322 · Cited by 21

A state-space formulation of a discontinuous Galerkin method for thermoacoustic stability analysis

Meindl, M., Albayrak, A., & Polifke, W. (2020) · Journal of Sound and Vibration · doi:10.1016/j.jsv.2020.115431 · Cited by 23

On the computation of a very large number of eigenvalues for selfadjoint elliptic operators by means of multigrid methods

Heuveline, V. (2003) · Journal of Computational Physics · doi:10.1016/s0021-9991(02)00043-8 · Cited by 23

A Note on the Calculation of Step-Lengths in Interior-Point Methods for Semidefinite Programming

Toh, K.-C. (2002) · Computational Optimization and Applications · doi:10.1023/a:1013777203597 · Cited by 23

A $QL$ Procedure for Computing the Eigenvalues of Complex Symmetric Tridiagonal Matrices

Cullum, J. K., & Willoughby, R. A. (1996) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479894137639 · Cited by 23

Spectrum of a non-self-adjoint operator associated with the periodic heat equation

Chugunova, M., & Pelinovsky, D. E. (2007) · Journal of Mathematical Analysis and Applications · doi:10.1016/j.jmaa.2007.12.036 · Cited by 23

Nonlinear Eigenproblems

Guillaume, P. (1999) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479897324172 · Cited by 23

Probing the existence of phase transitions in one-dimensional fluids of penetrable particles

Prestipino, S., Gazzillo, D., & Tasinato, N. (2015) · Physical Review E · doi:10.1103/physreve.92.022138 · Cited by 22

Development and Dynamical Analysis of Laboratory Facility Exhibiting Full-Scale Combustion Instability Characteristics

Quinlan, J. M., & Zinn, B. T. (2017) · AIAA Journal · doi:10.2514/1.j055680 · Cited by 22

A literature survey of matrix methods for data science

Stoll, M. (2020) · GAMM-Mitteilungen · doi:10.1002/gamm.202000013 · Cited by 25

A matrix-free isogeometric Galerkin method for Karhunen–Loève approximation of random fields using tensor product splines, tensor contraction and interpolation based quadrature

Mika, M., Hughes, T. J. R., Schillinger, D., et al. (2021) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2021.113730 · Cited by 22

The dominant instability of near-extreme Stokes waves

Deconinck, B., Dyachenko, S. A., Lushnikov, P. M., et al. (2023) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2308935120 · Cited by 22

An equation-free approach to agent-based computation: Bifurcation analysis and control of stationary states

Siettos, C. I., Gear, C. W., & Kevrekidis, I. G. (2012) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/99/48007 · Cited by 23

A Posteriori Error Bounds for Krylov-Based Fast Frequency Sweeps of Finite-Element Systems

Konkel, Y., Farle, O., Sommer, A., et al. (2014) · IEEE Transactions on Magnetics · doi:10.1109/tmag.2013.2285442 · Cited by 22

First principles multielectron mixed quantum/classical simulations in the condensed phase. I. An efficient Fourier-grid method for solving the many-electron problem

Glover, W. J., Larsen, R. E., & Schwartz, B. J. (2010) · The Journal of Chemical Physics · doi:10.1063/1.3352564 · Cited by 22

Fast Estimation of Approximate Matrix Ranks Using Spectral Densities

Ubaru, S., Saad, Y. E.-M., & Seghouane, A. (2017) · Neural Computation · doi:10.1162/neco_a_00951 · Cited by 22

Flows Generating Nonlinear Eigenfunctions

Nossek, R. Z., & Gilboa, G. (2017) · Journal of Scientific Computing · doi:10.1007/s10915-017-0577-6 · Cited by 22

Finite Element Method for Resonant Cavity Problem With Complex Geometrical Structure and Anisotropic Fully Conducting Media

Jiang, W., Liu, J., Xiong, X., et al. (2017) · IEEE Transactions on Microwave Theory and Techniques · doi:10.1109/tmtt.2017.2661740 · Cited by 22

Buckling of an Elastic Ridge: Competition between Wrinkles and Creases

Lestringant, C., Maurini, C., Lazarus, A., et al. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.165501 · Cited by 22

Vortex pairing in jets as a global Floquet instability: modal and transient dynamics

Shaabani-Ardali, L., Sipp, D., & Lesshafft, L. (2019) · Journal of Fluid Mechanics · doi:10.1017/jfm.2018.977 · Cited by 22

Iterative approaches to the self-consistent nuclear energy density functional problem

Ryssens, W., Bender, M., & Heenen, P.-H. (2019) · The European Physical Journal A · doi:10.1140/epja/i2019-12766-6 · Cited by 22

Computational issues in the simulation of semiconductor quantum wires

Trellakis, A., & Ravaioli, U. (2000) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/s0045-7825(99)00183-8 · Cited by 22

The density matrix renormalization group algorithm on kilo-processor architectures: Implementation and trade-offs

Nemes, C., Barcza, G., Nagy, Z., Legeza, Ö., & Szolgay, P. (2014) · Computer Physics Communications · doi:10.1016/j.cpc.2014.02.021 · Cited by 22

Matrix perturbation theory

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Matrix Computations

Golub, G. (2012) · doi:10.56021/9781421407944 · Cited by 34,505

Matrix Analysis

Horn, R. A., & Johnson, C. R. (1985) · Cited by 22,203

GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems

Saad, Y., & Schultz, M. H. (1986) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0907058 · Cited by 11,280

An iteration method for the solution of the eigenvalue problem of linear differential and integral operators

Lanczos, C. (1950) · Journal of research of the National Bureau of Standards · doi:10.6028/jres.045.026 · Cited by 4,356