Numerical Methods for Large Eigenvalue Problems: Revised Edition

Do Metrics Make Recommender Algorithms?

Campochiaro, E., Casatta, R., Cremonesi, P., et al. (2009) · International Conference on Advanced Information Networking and Applications Workshops (WAINA) · doi:10.1109/waina.2009.127 · Cited by 22

Numerical evaluation of SBmethod

Helmberg, C. (2003) · Mathematical Programming · doi:10.1007/s10107-002-0354-6 · Cited by 22

Self‐consistent hybrid approach for simulating electron transfer reactions in condensed phases

Wang, H., & Thoss, M. (2002) · Israel Journal of Chemistry · doi:10.1560/kj0g-kb9c-g0jb-area · Cited by 22

Hessenberg matrices in krylov subspaces and the computation of the spectrum

Nevanlinna, O. (1995) · Numerical Functional Analysis and Optimization · doi:10.1080/01630569508816627 · Cited by 22

Model-free voltage stability assessments via singular value analysis of PMU data

Lim, J. M., & DeMarco, C. L. (2013) · doi:10.1109/irep.2013.6629399 · Cited by 21

Complete radiation boundary conditions for the Helmholtz equation I: waveguides

Hagstrom, T. M., & Kim, S. (2019) · Numerische Mathematik · doi:10.1007/s00211-018-1012-0 · Cited by 21

Solving generalized inverse eigenvalue problems via L-BFGS-B method

Dalvand, Z., & Hajarian, M. (2020) · Inverse Problems in Science and Engineering · doi:10.1080/17415977.2020.1763982 · Cited by 21

Thermally Driven Flow of Water in Partially Heated Tall Vertical Concentric Annulus

Mustafa, J., Alqaed, S., & Siddiqui, M. A. (2020) · Entropy · doi:10.3390/e22101189 · Cited by 21

Nucleus size and its effect on nucleosome stability in living cells

Efremov, A. K., Hovan, L., & Yan, J. (2022) · Biophysical Journal · doi:10.1016/j.bpj.2022.09.019 · Cited by 21

Vortex-induced vibration of a two degree-of-freedom flexibly mounted circular cylinder in the crossflow direction

Mousavisani, S., Chowdhury, N. N., Samsam-Khayani, H., et al. (2022) · Journal of Fluid Mechanics · doi:10.1017/jfm.2022.893 · Cited by 21

Nonbacktracking Spectral Clustering of Nonuniform Hypergraphs

Chodrow, P. S., Eikmeier, N., & Haddock, J. (2023) · SIAM Journal on Mathematics of Data Science · doi:10.1137/22m1494713 · Cited by 22

Bipartite quantum states and random complex networks

Garnerone, S., Giorda, P., & Paolo Zanardi, A. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/1/013011 · Cited by 23

A memory-efficient model order reduction for time-delay systems

Zhang, Y., & Su, Y. (2013) · BIT Numerical Mathematics · doi:10.1007/s10543-013-0439-z · Cited by 21

From steady solutions to chaotic flows in a Rayleigh–Bénard problem at moderate Rayleigh numbers

Puigjaner, D., Herrero, J., Simó, C., et al. (2011) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2011.01.007 · Cited by 21

Macroscopic optical response and photonic bands

Pérez-Huerta, J. S., Ortiz, G. P., Mendoza, B. S., et al. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/4/043037 · Cited by 21

Acceleration of the Arnoldi method and real eigenvalues of the non-Hermitian Wilson–Dirac operator

Bergner, G., & Wuilloud, J. (2011) · Computer Physics Communications · doi:10.1016/j.cpc.2011.10.007 · Cited by 21

The implicit application of a rational filter in the RKS method

Samblanx, G. D., Meerbergen, K., & Bultheel, A. (1997) · BIT Numerical Mathematics · doi:10.1007/bf02510361 · Cited by 21

Improved inversion algorithms for near-surface characterization

Astaneh, A. V., & Guddati, M. N. (2016) · Geophysical Journal International · doi:10.1093/gji/ggw192 · Cited by 21

A FEAST algorithm with oblique projection for generalized eigenvalue problems

Yin, G., Chan, R. H.-F., & Yeung, M.-C. (2017) · Numerical Linear Algebra with Applications · doi:10.1002/nla.2092 · Cited by 21

Intrinsic and extrinsic operators for shape analysis

Wang, Y., & Solomon, J. (2019) · Handbook of numerical analysis · doi:10.1016/bs.hna.2019.08.003 · Cited by 23

Prior-Preconditioned Conjugate Gradient Method for Accelerated Gibbs Sampling in “Large n , Large p ” Bayesian Sparse Regression

Nishimura, A., & Suchard, M. A. (2022) · Journal of the American Statistical Association · doi:10.1080/01621459.2022.2057859 · Cited by 35

PFEAST: A High Performance Sparse Eigenvalue Solver Using Distributed-Memory Linear Solvers

Kestyn, J., Kalantzis, V., Polizzi, E., et al. (2016) · 2012 International Conference for High Performance Computing, Networking, Storage and Analysis · doi:10.1109/sc.2016.15 · Cited by 21

Three-dimensional transport calculation of multiple alpha modes in subcritical systems

Kópházi, J., & Lathouwers, D. (2012) · Annals of Nuclear Energy · doi:10.1016/j.anucene.2012.06.021 · Cited by 21

A thick-restarted block Arnoldi algorithm with modified Ritz vectors for large eigenproblems

Jiang, W., & Wu, G. (2010) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2010.05.034 · Cited by 21

Rank-One Corrections of Nonnegative Matrices, With an Application to Matrix Population Models

Protasov, V. Y., & Logofet, D. O. (2014) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/130935537 · Cited by 21

Cluster robustness of preconditioned gradient subspace iteration eigensolvers

Ovtchinnikov, E. (2005) · Linear Algebra and its Applications · doi:10.1016/j.laa.2005.06.039 · Cited by 21

Modal Decomposition Method for BWR Stability Analysis.

Verdú, G., Ginestar, D., Vidal, V., et al. (1998) · Journal of Nuclear Science and Technology · doi:10.3327/jnst.35.538 · Cited by 21

Robust finite-element solution of lossy and unbounded electromagnetic eigenvalue problems

Zhu, Y., & Cangellaris, A. C. (2002) · IEEE Transactions on Microwave Theory and Techniques · doi:10.1109/tmtt.2002.803425 · Cited by 21

The quasi-independent curvilinear coordinate approximation for geometry optimization

Németh, K., & Challacombe, M. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1771636 · Cited by 21

Is Jacobi--Davidson Faster than Davidson?

Notay, Y. (2004) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479803430941 · Cited by 21

Quantum Combinatorial Optimization in the NISQ Era: A Systematic Mapping Study

Gemeinhardt, F., Garmendia, A., Wimmer, M., Weder, B., & Leymann, F. (2024) · ACM Computing Surveys · doi:10.1145/3620668 · Cited by 22

Solving Most Systems of Random Quadratic Equations

Wang, G., Giannakis, G. B., Saad, Y. E.-M., et al. (2017) · neural information processing systems · Cited by 20

ChASE

Winkelmann, J., Springer, P., & Napoli, E. D. (2019) · ACM Transactions on Mathematical Software · doi:10.1145/3313828 · Cited by 20

A Subspace-Splitting Moment-Matching Model-Order Reduction Technique for Fast Wideband FEM Simulations of Microwave Structures

Szypulski, D., Fotyga, G., de la Rubia, V., et al. (2020) · IEEE Transactions on Microwave Theory and Techniques · doi:10.1109/tmtt.2020.3001627 · Cited by 20

Eigenvalue problem derivatives computation for a complex matrix using the adjoint method

He, S., Shi, Y., Jonsson, E., et al. (2022) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2022.109717 · Cited by 20

Equation-Free multiscale computational analysis of individual-based epidemic dynamics on networks

Siettos, C. I. (2011) · Applied Mathematics and Computation · doi:10.1016/j.amc.2011.05.067 · Cited by 20

Performance comparison of parallel eigensolvers based on a contour integral method and a Lanczos method

Yamazaki, I., Tadano, H., Sakurai, T., et al. (2012) · Parallel Computing · doi:10.1016/j.parco.2012.04.001 · Cited by 20

A DEGREE SELECTION METHOD OF MATRIX CONDENSATIONS FOR EIGENVALUE PROBLEMS

LI, W. (2002) · Journal of Sound and Vibration · doi:10.1006/jsvi.2002.5336 · Cited by 20

Convergence analysis of Lanczos-type methods for the linear response eigenvalue problem

Teng, Z., & Li, R. (2013) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2013.01.003 · Cited by 20

Computable upper and lower bounds on eigenfrequencies

Wang, L., Chamoin, L., Pierre Ladevèze, B., et al. (2016) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2016.01.002 · Cited by 20

A parallel and streaming Dynamic Mode Decomposition algorithm with finite precision error analysis for large data

Anantharamu, S., & Mahesh, K. (2019) · Journal of Computational Physics · doi:10.1016/j.jcp.2018.12.012 · Cited by 20

Comparison of PCA approaches for very large group ICA

Calhoun, V. D., Silva, R. F., Adalı, T., et al. (2015) · NeuroImage · doi:10.1016/j.neuroimage.2015.05.047 · Cited by 20

Augmented Block Householder Arnoldi Method

Baglama, J. (2008) · Linear Algebra and its Applications · doi:10.1016/j.laa.2007.12.021 · Cited by 20

An isogeometric collocation method for efficient random field discretization

Jahanbin, R., & Rahman, S. (2018) · International Journal for Numerical Methods in Engineering · doi:10.1002/nme.5959 · Cited by 20

Composite orthogonal projection methods for large matrix eigenproblems

Jia, Z. (1989) · Science in China Series A Mathematics · doi:10.1007/bf02880075 · Cited by 20

Symmetry-adapted distributed approximating functionals: Theory and application to the ro-vibrational states of H3+

Iyengar, S. S., Parker, G. A., Kouri, D. J., et al. (1999) · The Journal of Chemical Physics · doi:10.1063/1.478962 · Cited by 20

Analysis of discrete-to-discrete imaging models for iterative tomographic image reconstruction and compressive sensingPreprint

Jørgensen, J. S., Sidky, E. Y., & Pan, X. (2011) · arXiv (Cornell University) · Cited by 20

Koopman Neural Operator as a Mesh-Free Solver of Non-Linear Partial Differential EquationsPreprint

Xiong, W., Huang, X., Zhang, Z., Deng, R., Sun, P., & Tian, Y. (2023) · SSRN Electronic Journal · doi:10.2139/ssrn.4479919 · Cited by 20

Effects of impurity and cross-sectional shape on entropy of quantum wires

Khordad, R., Sedehi, H. R. R., & Bahramiyan, H. (2018) · Journal of Computational Electronics · doi:10.1007/s10825-018-1133-9 · Cited by 19

Superharmonic instability of stokes waves

Korotkevich, A. O., Lushnikov, P. M., Semenova, A., et al. (2022) · Studies in Applied Mathematics · doi:10.1111/sapm.12535 · Cited by 19

A posteriori error analysis of component mode synthesis for the elliptic eigenvalue problem

Jakobsson, H., & Larson, M. G. (2011) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2011.05.002 · Cited by 19

Topological aspects of fermions on a honeycomb lattice

Chakrabarti, D., Hands, S., & Antonio Rago, A. (2009) · Journal of High Energy Physics · doi:10.1088/1126-6708/2009/06/060 · Cited by 19

Emerging Intuitionistic Fuzzy Classifiers for Intrusion Detection System

Kavitha, B., Subramanian, K., & Sheeba Maybell, P. (2011) · Journal of Advances in Information Technology · doi:10.4304/jait.2.2.99-108 · Cited by 19

A Sylvester–Arnoldi type method for the generalized eigenvalue problem with two‐by‐two operator determinants

Meerbergen, K., & Plestenjak, B. (2015) · Numerical Linear Algebra with Applications · doi:10.1002/nla.2005 · Cited by 19

New Algorithms for Computing the Real Structured Pseudospectral Abscissa and the Real Stability Radius of Large and Sparse Matrices

Rostami, M. W. (2015) · SIAM Journal on Scientific Computing · doi:10.1137/140975413 · Cited by 19

A note on measure-geometric Laplacians

Keßeböhmer, M., Samuel, T., & Weyer, H. (2016) · Monatshefte für Mathematik · doi:10.1007/s00605-016-0906-0 · Cited by 19

Elastic rods with incompatible strain: Macroscopic versus microscopic buckling

Lestringant, C., & Audoly, B. (2016) · Journal of the Mechanics and Physics of Solids · doi:10.1016/j.jmps.2016.12.001 · Cited by 19

PFEAST: a high performance sparse eigenvalue solver using distributed-memory linear solvers

Kestyn, J., Kalantzis, V., Polizzi, E., et al. (2016) · doi:10.5555/3014904.3014926 · Cited by 19

A New Family of Exponential-Based High-Order DGTD Methods for Modeling 3-D Transient Multiscale Electromagnetic Problems

Wang, H., Xu, L., Li, B., et al. (2017) · IEEE Transactions on Antennas and Propagation · doi:10.1109/tap.2017.2752223 · Cited by 19

Computing eigenpairs in augmented Krylov subspace produced by Jacobi–Davidson correction equation

Miao, C.-Q. (2018) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2018.05.001 · Cited by 19

Excited-State Spectra of Strongly Correlated Molecules from a Reduced-Density-Matrix Approach

Hemmatiyan, S., Sajjan, M., Schlimgen, A. W., et al. (2018) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.8b02455 · Cited by 19

FEAST for Differential Eigenvalue Problems

Horning, A., & Townsend, A. (2020) · SIAM Journal on Numerical Analysis · doi:10.1137/19m1238708 · Cited by 19

Extreme Eigenvalues-Based Detectors for Spectrum Sensing in Cognitive Radio Networks

Zhao, W., Ali, S. S., Jin, M., et al. (2021) · IEEE Transactions on Communications · doi:10.1109/tcomm.2021.3121426 · Cited by 19

Further Analysis of the Arnoldi Process for Eigenvalue Problems

Bellalij, M., Saad, Y. E.-M., & Sadok, H. (2010) · SIAM Journal on Numerical Analysis · doi:10.1137/070711487 · Cited by 19

On a self-consistent-field-like iteration for maximizing the sum of the Rayleigh quotients

Zhang, L. (2013) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2013.08.005 · Cited by 19

Quantum mechanical transition state theory and tunneling corrections

Thompson, W. H. (1999) · The Journal of Chemical Physics · doi:10.1063/1.478304 · Cited by 19

Feasible Barzilai–Borwein-like methods for extreme symmetric eigenvalue problems

Jiang, B., & Dai, Y.-H. (2012) · Optimization methods & software · doi:10.1080/10556788.2012.656115 · Cited by 19

Quantum dynamics of unimolecular dissociation reaction HFCO→HF+CO

Yamamoto, T., & Kato, S. (1998) · The Journal of Chemical Physics · doi:10.1063/1.477648 · Cited by 19

All-Atom Calculation of the Normal Modes of Bacteriorhodopsin Using a Sliding Block Iterative Diagonalization Method

Kaledin, A. L., Kaledin, M., & Bowman, J. M. (2005) · Journal of Chemical Theory and Computation · doi:10.1021/ct050161z · Cited by 19

An efficient first‐principle approach for electronic structures calculations of nanomaterials

Gao, B., Jiang, J., Liu, K., et al. (2007) · Journal of Computational Chemistry · doi:10.1002/jcc.20799 · Cited by 19

Computation of a Few Small Eigenvalues of a Large Matrix with Application to Liquid Crystal Modeling

Baglama, J., Calvetti, D., Reichel, L., et al. (1998) · Journal of Computational Physics · doi:10.1006/jcph.1998.6064 · Cited by 19

The sensitivity and stability of spinning process using frequency response method

Jung, H. W., Lee, J., Scriven, L. E., et al. (2004) · Korean Journal of Chemical Engineering · doi:10.1007/bf02705376 · Cited by 19

Graph Spectra and Modal Dynamics of Oscillatory Networks

Ayazifar, B. (2002) · DSpace@MIT (Massachusetts Institute of Technology) · Cited by 19

Subsampling Algorithms for Semidefinite ProgrammingPreprint

d’Aspremont, A. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0803.1990 · Cited by 19

AI-Based Model Order Reduction Techniques: A Survey

Mallick, S., & Mittal, M. (2025) · Archives of Computational Methods in Engineering · doi:10.1007/s11831-024-10207-2 · Cited by 21

A Direct Eigenanalysis of Multibody System in Equilibrium

Yang, C. G., Cao, D., Zhao, Z., et al. (2012) · Journal of Applied Mathematics · doi:10.1155/2012/638546 · Cited by 18

Krylov eigenvalue strategy using the FEAST algorithm with inexact system solves

Gavin, B., & Polizzi, E. (2018) · Numerical Linear Algebra with Applications · doi:10.1002/nla.2188 · Cited by 18

Nonlinear eigenvalue analysis for spectral element method

Mukherjee, A., Sarkar, S., & Banerjee, A. (2020) · Computers & Structures · doi:10.1016/j.compstruc.2020.106367 · Cited by 18

A New Hardware-Efficient Spectrum-Sensor VLSI Architecture for Data-Fusion-Based Cooperative Cognitive-Radio Network

Chaurasiya, R. B., & Shrestha, R. (2021) · IEEE Transactions on Very Large Scale Integration (VLSI) Systems · doi:10.1109/tvlsi.2021.3055344 · Cited by 18

Nishimori meets Bethe: a spectral method for node classification in sparse weighted graphs

Dall’Amico, L., Couillet, R., & Tremblay, N. (2021) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/ac21d3 · Cited by 18

Radial collocation methods for the onset of convection in rotating spheres

Sánchez, J., Garcia, F., & Net, M. (2015) · Journal of Computational Physics · doi:10.1016/j.jcp.2015.12.040 · Cited by 18

Space-Dependent Wielandt Shifts for Multigroup Diffusion Eigenvalue Problems

Yee, B. C., Kochunas, B. M., Larsen, E. W., et al. (2017) · Nuclear Science and Engineering · doi:10.1080/00295639.2017.1350001 · Cited by 18

Spatial modes for the neutron diffusion equation and their computation

Carreño, A., Vidal-Ferràndiz, A., Ginestar, D., et al. (2017) · Annals of Nuclear Energy · doi:10.1016/j.anucene.2017.08.018 · Cited by 18

A fully coupled two‐level Schwarz preconditioner based on smoothed aggregation for the transient multigroup neutron diffusion equations

Kong, F., Wang, Y., Schunert, S., et al. (2018) · Numerical Linear Algebra with Applications · doi:10.1002/nla.2162 · Cited by 18

Eigenmodes of Surface Energies for Shape Analysis

Hildebrandt, K., Schulz, C., von Tycowicz, C., et al. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-13411-1_20 · Cited by 18

A Combined TSA-SPA Algorithm for Computing Most Sensitive Eigenvalues in Large-Scale Power Systems

Chung, C. Y., & Dai, B. (2012) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2012.2202407 · Cited by 18

Using the Jacobi–Davidson method to obtain the dominant Lambda modes of a nuclear power reactor

Verdú, G., Ginestar, D., Miró, R., et al. (2005) · Annals of Nuclear Energy · doi:10.1016/j.anucene.2005.03.002 · Cited by 18

A timestepper-based approach for the coarse-grained analysis of microscopic neuronal simulators on networks: Bifurcation and rare-events micro- to macro-computations

Spiliotis, K., & Siettos, C. I. (2011) · Neurocomputing · doi:10.1016/j.neucom.2011.06.018 · Cited by 17

Complex dispersion relation calculations with the symmetric interior penalty method

Engström, C., & Wang, M. (2010) · International Journal for Numerical Methods in Engineering · doi:10.1002/nme.2926 · Cited by 18

Numerical Analysis of a New Mixed Formulation for Eigenvalue Convection-Diffusion Problems

Pierre, C., & Plouraboué, F. (2009) · SIAM Journal on Applied Mathematics · doi:10.1137/080736442 · Cited by 18

Computing the entropy of a large matrix

Wihler, T. P., Bessire, B., & Stefanov, A. (2014) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/47/24/245201 · Cited by 18

On the Lanczos and Golub–Kahan reduction methods applied to discrete ill‐posed problems

Gazzola, S., Onunwor, E., Reichel, L., et al. (2015) · Numerical Linear Algebra with Applications · doi:10.1002/nla.2020 · Cited by 18

A GMRES-Power algorithm for computing PageRank problems

Gu, C., Jiang, X.-L., Shao, C., et al. (2018) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2018.03.017 · Cited by 18

Convergence Estimates for the Generalized Davidson Method for Symmetric Eigenvalue Problems I: The Preconditioning Aspect

Ovtchinnikov, E. (2003) · SIAM Journal on Numerical Analysis · doi:10.1137/s0036142902411756 · Cited by 18

Structure and stability of non-symmetric Burgers vortices

Prochazka, A. O., & Pullin, D. I. (1998) · Journal of Fluid Mechanics · doi:10.1017/s0022112098008866 · Cited by 18

Some computational improvements in process system reliability and safety analysis using dynamic methodologies

Belhadj, M., & Aldemir, T. (1996) · Reliability Engineering & System Safety · doi:10.1016/0951-8320(95)00144-1 · Cited by 18

Modal Decomposition Method for-BWR Stability Analysis

Verdú, G., Ginestar, D., Vidal, V., et al. (1998) · Journal of Nuclear Science and Technology · doi:10.1080/18811248.1998.9733907 · Cited by 18

Electrostatic binding energy calculation using the finite difference solution to the linearized Poisson-Boltzmann equation: Assessment of its accuracy

Shen, J. H., & Wendoloski, J. J. (1996) · Journal of Computational Chemistry · doi:10.1002/(sici)1096-987x(199602)17:3 · Cited by 37

Efficient first-principles calculations of the electronic structure of periodic systems

Alemany, M. M. G., Jain, M., Tiago, M. L., et al. (2007) · Computer Physics Communications · doi:10.1016/j.cpc.2007.04.003 · Cited by 18

Torsional flow: elastic instability in a finite domain

Avagliano, A., & Phan-Thien, N. (1996) · Journal of Fluid Mechanics · doi:10.1017/s0022112096002005 · Cited by 18

Matrix perturbation theory

(1991) · Mathematics and Computers in Simulation · doi:10.1016/0378-4754(91)90038-5 · Cited by 2,474

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