Numerical Methods for Large Eigenvalue Problems: Revised Edition

Krylov space approximate Kalman filtering

Bardsley, J. M., Parker, A. E., Solonen, A., et al. (2011) · Numerical Linear Algebra with Applications · doi:10.1002/nla.805 · Cited by 14

Diffraction Modeling of the Multicore Fiber Amplifier

Elkin, N. N., Napartovich, A. P., Troshchieva, V. N., et al. (2007) · Journal of Lightwave Technology · doi:10.1109/jlt.2007.901517 · Cited by 14

A rank‐exploiting infinite Arnoldi algorithm for nonlinear eigenvalue problems

Beeumen, R. V., Jarlebring, E., & Michiels, W. (2016) · Numerical Linear Algebra with Applications · doi:10.1002/nla.2043 · Cited by 14

Performance Analysis and Optimization of Sparse Matrix-Vector Multiplication on Intel Xeon Phi

Elafrou, A., Goumas, G., & Koziris, N. (2017) · IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW) · doi:10.1109/ipdpsw.2017.134 · Cited by 14

Aperture Distributions for Maximum Endfire Directivity From a Continuous Line Source With a Uniform Phase Progression

Liu, J., & Jackson, D. R. (2017) · IEEE Transactions on Antennas and Propagation · doi:10.1109/tap.2017.2742538 · Cited by 14

Beyond Automated Multilevel Substructuring: Domain Decomposition with Rational Filtering

Kalantzis, V., Xi, Y., & Saad, Y. E.-M. (2018) · SIAM Journal on Scientific Computing · doi:10.1137/17m1154527 · Cited by 14

Electronic Structure of Quantum Dots

Hines, C., McCarthy, S. P., Wang, J. B., et al. (2002) · UWA Profiles and Research Repository (University of Western Australia) · Cited by 14

Implementation of a variable block Davidson method with deflation for solving large sparse eigenproblems

Sadkane, M., & Sidje, R. B. (1999) · Numerical Algorithms · doi:10.1023/a:1019199700323 · Cited by 14

HQS@HPC: Comparative numerical study of Anderson localisation in disordered electron systems

Schubert, G., Weiße, A., Wellein, G., et al. (2005) · Springer eBooks · doi:10.1007/3-540-28555-5_21 · Cited by 14

Theoretical study of the double Renner effect for AΠ2 MgNC∕MgCN: Higher excited rovibrational states

Odaka, T. E., Melnikov, V. V., Jensen, P., et al. (2007) · The Journal of Chemical Physics · doi:10.1063/1.2464094 · Cited by 14

Time evolution in the unimolecular master equation at low temperatures: full spectral solution with scalable iterative methods and high precision

Frankcombe, T. J., & Smith, S. C. (2001) · Computer Physics Communications · doi:10.1016/s0010-4655(01)00298-3 · Cited by 14

Perturbation-based Markovian Transmission Model for Probing Allosteric Dynamics of Large Macromolecular Assembling: A Study of GroEL-GroES

Lu, H., & Liang, J. (2009) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000526 · Cited by 14

Conjugate-gradient eigenvalue solvers in computing electronic properties of nanostructure architectures

Tomov, S. Z., Langou, J., Dongarra, J. J., et al. (2006) · International Journal of Computational Science and Engineering · doi:10.1504/ijcse.2006.012774 · Cited by 14

Time-domain channel equalizer design using the inverse power method

Chiu, W.-M., Tsai, W. K., Liau, T. C., et al. (2003) · International Conference on Communications · doi:10.1109/icc.1999.765418 · Cited by 14

Fixed-Polynomial Approximate Spectral Transformations for Preconditioning the Eigenvalue Problem

Thornquist, H. (2006) · Rice Research Repository (Rice University) · Cited by 14

Metastability of Markovian systems

Huisinga, W. (2001) · Universitätsbibliothek der FU Berlin Hochschulschriftenstelle u. Dokumentenserver · doi:10.17169/refubium-9957 · Cited by 14

Model Reduction for Piezo-Mechanical Systems Using Balanced Truncation

Uddin, M. M. (2011) · Qucosa - Monarch (Chemnitz University of Technology) · Cited by 14

Stochastic Canonical Correlation AnalysisPreprint

Gao, C., Garber, D., Srebro, N., et al. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1702.06533 · Cited by 14

Uncertainty Quantification for In Silico Chemistry

Frömbgen, T., Surzhikova, E., Dölz, J., Proppe, J., Kirchner, B., & Jacob, C. R. (2026) · Chemical Reviews · doi:10.1021/acs.chemrev.5c00931 · Cited by 18

A posteriori error estimation for the non-self-consistent Kohn–Sham equations

Herbst, M. F., Levitt, A., & Eric Cancès, B. (2020) · Faraday Discussions · doi:10.1039/d0fd00048e · Cited by 20

Variational-Based Reduced-Order Model in Dynamic Substructuring of Coupled Structures Through a Dissipative Physical Interface: Recent Advances

Ohayon, R., Soize, C., & Sampaio, R. (2014) · Archives of Computational Methods in Engineering · doi:10.1007/s11831-014-9107-y · Cited by 13

Spectral properties of dynamic processes in a nuclear reactor

Avvakumov, A. V., Strizhov, V. F., Vabishchevich, P. N., et al. (2016) · Annals of Nuclear Energy · doi:10.1016/j.anucene.2016.09.021 · Cited by 13

A stopping criterion for the iterative solution of partial differential equations

Rao, K. J., Malan, P., & Perot, B. (2017) · Journal of Computational Physics · doi:10.1016/j.jcp.2017.09.033 · Cited by 13

Computing Eigenvalues of Diagonalizable Matrices on a Quantum Computer

Shao, C. (2022) · ACM Transactions on Quantum Computing · doi:10.1145/3527845 · Cited by 16

Randomized block Krylov subspace methods for trace and log-determinant estimators

Li, H., & Zhu, Y. (2021) · BIT Numerical Mathematics · doi:10.1007/s10543-021-00850-7 · Cited by 13

Numerical Exploration of Oscillation Modes in Rapidly Rotating Stars

Ballot, J., Lignières, F., & Reese, D. R. (2012) · Lecture notes in physics · doi:10.1007/978-3-642-33380-4_5 · Cited by 13

Liquid Sloshing Damping in an Elastic Container

Miras, T., Schotté, J., & Ohayon, R. (2011) · Journal of Applied Mechanics · doi:10.1115/1.4005189 · Cited by 13

Spectral Power Iterations for the Random Eigenvalue Problem

Meidani, H., & Ghanem, R. (2014) · AIAA Journal · doi:10.2514/1.j051849 · Cited by 13

Asymmetries in production of He +(n=2) with an intense few-cycle attosecond pulse

Djiokap, J. M. N., Hu, S. X., Jiang, W., et al. (2013) · Physical Review A · doi:10.1103/physreva.88.011401 · Cited by 13

Fast Orthonormal Sparsifying Transforms Based on Householder Reflectors

Rusu, C., Prelcic, N. G., & Heath, R. W. (2016) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2016.2612168 · Cited by 13

Accuracy of singular vectors obtained by projection-based SVD methods

Nakatsukasa, Y. (2017) · BIT Numerical Mathematics · doi:10.1007/s10543-017-0665-x · Cited by 12

A Fast Contour-Integral Eigensolver for Non-Hermitian Matrices

Ye, X., Xia, J., Chan, R. H., et al. (2017) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/16m1086601 · Cited by 13

Fluid–solid Floquet stability analysis of self-propelled heaving foils

Ramos, L. B., Marquet, O., Bergmann, M., & Iollo, A. (2021) · Journal of Fluid Mechanics · doi:10.1017/jfm.2020.1021 · Cited by 13

Global stability and nonlinear dynamics of wake flows with a two-fluid interface

Schmidt, S., Tammisola, O., Lesshafft, L., et al. (2021) · Journal of Fluid Mechanics · doi:10.1017/jfm.2021.150 · Cited by 13

The Hierarchical Subspace Iteration Method for Laplace–Beltrami Eigenproblems

Nasikun, A., & Hildebrandt, K. (2022) · ACM Transactions on Graphics · doi:10.1145/3495208 · Cited by 13

Combined tank and applicator design of radio frequency heating systems

Neophytou, R. I., & Metaxas, A. C. (1999) · IEE Proceedings - Microwaves Antennas and Propagation · doi:10.1049/ip-map:19990664 · Cited by 13

Effect of spectral range on convergence in Lanczos algorithm, a numerical study

Chen, R., & Guo, H. (2003) · Chemical Physics Letters · doi:10.1016/s0009-2614(02)02040-7 · Cited by 13

Eigenmode Analysis and Reduced-Order Modeling of Unsteady Transonic Potential Flow Around Airfoils

Florea, R. V., Hall, K. C., & Dowell, E. H. (2000) · Journal of Aircraft · doi:10.2514/2.2619 · Cited by 13

Dynamic Characterization and Stability of a Large Size Multibody Tiltrotor Model by POD Analysis

Masarati, P., Quaranta, G., Lanz, M., et al. (2003) · doi:10.1115/detc2003/vib-48440 · Cited by 13

Progress in the numerical solution of the nonsymmetric eigenvalue problem

Bai, Z. (1995) · Numerical Linear Algebra with Applications · doi:10.1002/nla.1680020304 · Cited by 13

A Parallel Davidson-Type Algorithm for Several Eigenvalues

Borges, L., & Oliveira, S. (1998) · Journal of Computational Physics · doi:10.1006/jcph.1998.6003 · Cited by 13

Exclusion and Inclusion Regions for the Eigenvalues of a Normal Matrix

Huhtanen, M., & Larsen, R. M. (2002) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479801384561 · Cited by 13

Remarks on large-scale matrix diagonalization using a Lagrange-Newton-Raphson minimization in a subspace

Anglada, J. M., Besalú, E., & Bofill, J. M. (1999) · Theoretical Chemistry Accounts · doi:10.1007/s002140050527 · Cited by 13

Noise-free spectrum for time-dependent calculation of eigenenergies

Dai, J., & Zhang, J. Z. H. (1995) · The Journal of Chemical Physics · doi:10.1063/1.469770 · Cited by 13

Changing poles in the rational Lanczos method for the Hermitian eigenvalue problem

Meerbergen, K. (2000) · Numerical Linear Algebra with Applications · doi:10.1002/1099-1506(200101/02)8:1 · Cited by 13

Eigenvalue estimation of differential operators with a quantum algorithm

Szkopek, T., Roychowdhury, V., Yablonovitch, E., et al. (2005) · Physical Review A · doi:10.1103/physreva.72.062318 · Cited by 13

Quadratic Optimization with Orthogonality Constraints: Explicit Lojasiewicz Exponent and Linear Convergence of Line-Search MethodsPreprint

Liu, H., Wu, W., & So, A. M. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1510.01025 · Cited by 13

Merging of feature tracks for camera motion estimation from video

Thormählen, T., Hasler, N., Wand, M. D., et al. (2008) · doi:10.1049/cp:20081079 · Cited by 13

Solving Almost all Systems of Random Quadratic EquationsPreprint

Wang, G., Giannakis, G. B., Saad, Y. E.-M., et al. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1705.10407 · Cited by 13

Direct numerical simulations of the κ-mechanism I. Radial modes in the purely radiative casePreprint

Gastine, T., & Dintrans, B. (2008) · Cited by 13

Evaporating sessile droplets: solutal Marangoni effects overwhelm thermal Marangoni flow

Rocha, D., Lederer, P. L., Dekker, P. J., et al. (2025) · Journal of Fluid Mechanics · doi:10.1017/jfm.2025.10208 · Cited by 12

FPGA-Based Sparse Matrix Multiplication Accelerators: From State-of-the-Art to Future Opportunities

Liu, Y., Chen, R., Li, S., et al. (2024) · ACM Transactions on Reconfigurable Technology and Systems · doi:10.1145/3687480 · Cited by 12

On Rayleigh Quotient Iteration for the Dual Quaternion Hermitian Eigenvalue Problem

Duan, S., Wang, Q., & Duan, X. (2024) · Mathematics · doi:10.3390/math12244006 · Cited by 12

Efficient numerical calculation of drift and diffusion coefficients in the diffusion approximation of kinetic equations

Bonnaillie‐Noël, V., Carrillo, J. A., Goudon, T., et al. (2016) · IMA Journal of Numerical Analysis · doi:10.1093/imanum/drv066 · Cited by 12

Preconditioned Locally Harmonic Residual Method for Computing Interior Eigenpairs of Certain Classes of Hermitian Matrices

Vecharynski, E., & Knyazev, A. (2015) · SIAM Journal on Scientific Computing · doi:10.1137/14098048x · Cited by 12

Generalized eigenvalue proximal support vector regressor

Rastogi, R., Karpatne, A., & Chandra, S. (2011) · Expert Systems with Applications · doi:10.1016/j.eswa.2011.04.121 · Cited by 12

Inferring Gene Regulatory Networks by Combining Supervised and Unsupervised Methods

Turki, T., Wang, J. T. L., & Rajikhan, I. (2016) · IEEE International Conference on Machine Learning and Applications (ICMLA) · doi:10.1109/icmla.2016.0031 · Cited by 12

ROSC

Li, X., Kao, B., Luo, S., et al. (2018) · doi:10.1145/3178876.3185993 · Cited by 12

Spectral and Modal Methods for Studying Stability and Control of Electric Power Systems

VOROPAI, N. I., Golub, I. I., Efimov, D. N., Iskakov, A. B., & Yadykin, I. B. (2020) · Automation and Remote Control · doi:10.1134/s000511792010001x · Cited by 12

Machine learning based prediction of the electronic structure of quasi-one-dimensional materials under strain

Pathrudkar, S., Yu, H. M., Ghosh, S., & Banerjee, A. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.105.195141 · Cited by 16

h-, p-, and hp-Versions of the Least-Squares Collocation Method for Solving Boundary Value Problems for Biharmonic Equation in Irregular Domains and Their Applications

Belyaev, V. A., Брындин, Л. С., Golushko, S., et al. (2022) · Computational Mathematics and Mathematical Physics · doi:10.1134/s0965542522040029 · Cited by 12

Performance Modelling and Markov Chains

Stewart, W. J. (2007) · Springer eBooks · doi:10.1007/978-3-540-72522-0_1 · Cited by 12

CAS Application to the Construction of the Collocations and Least Residuals Method for the Solution of 3D Navier–Stokes Equations

Shapeev, V. P., & Vorozhtsov, E. V. (2013) · Lecture notes in computer science · doi:10.1007/978-3-319-02297-0_31 · Cited by 12

Bounds for the Rayleigh Quotient and the Spectrum of Self-Adjoint Operators

Zhu, P., Argentati, M. E., & Knyazev, A. (2013) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/120884468 · Cited by 12

A reflection on the implicitly restarted Arnoldi method for computing eigenvalues near a vertical line

Meerbergen, K., & Vandebril, R. (2011) · Linear Algebra and its Applications · doi:10.1016/j.laa.2011.07.020 · Cited by 12

Static-field-induced states and their manifestation in tunneling ionization dynamics of molecules

Jiang, W., Tolstikhin, O. I., Peng, L.-Y., et al. (2012) · Physical Review A · doi:10.1103/physreva.85.023404 · Cited by 12

Self-avoiding polygons and walks in slits

Alvarez, J., van Rensburg, E. J. J., Soteros, C. E., et al. (2008) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/41/18/185004 · Cited by 12

Inverse eigenvalue problems for extended Hessenberg and extended tridiagonal matrices

Mach, T., Barel, M. V., & Vandebril, R. (2014) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2014.03.015 · Cited by 12

Acceleration of the determination of periodic states of cyclically operated reactors and separators

van Noorden, T. L., Lunel, S. M. V., & Bliek, A. (2002) · Chemical Engineering Science · doi:10.1016/s0009-2509(01)00431-6 · Cited by 12

Implementation and use of a direct, partially integral‐driven non‐Dyson propagator method for molecular ionization

Storchi, L., Vitillaro, G., & Tarantelli, F. (2008) · Journal of Computational Chemistry · doi:10.1002/jcc.21104 · Cited by 12

Pressure Bifurcation Phenomenon on Supersonic Blowing Trailing Edges

Martinez-Cava, A., Wang, Y., de Vicente, J., et al. (2018) · AIAA Journal · doi:10.2514/1.j057056 · Cited by 12

PairDiag: An exact diagonalization program for solving general pairing Hamiltonians

Liu, X., & Qi, C. (2020) · Computer Physics Communications · doi:10.1016/j.cpc.2020.107349 · Cited by 12

Destabilization of a laminar flow in a rectangular channel by transversely-oriented wall corrugation

Szumbarski, J., & Błoński, S. (2010) · DOAJ (DOAJ: Directory of Open Access Journals) · doi:10.24423/aom.413 · Cited by 12

Infrared Spectra of a Model Phenol-Amine Proton Transfer Complex in Nanoconfined CH3Cl

Mitchell‐Koch, K. R., & Thompson, W. H. (2008) · The Journal of Physical Chemistry B · doi:10.1021/jp076714e · Cited by 12

Parallel implementations of the trace minimization scheme TraceMIN for the sparse symmetric eigenvalue problem

Klinvex, A., Saied, F., & Sameh, A. (2012) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2012.06.011 · Cited by 12

Analysis of a Minimum Perturbation Algorithm for Nonsymmetric Linear Systems

Kasenally, E. M., & Simoncini, V. (1997) · SIAM Journal on Numerical Analysis · doi:10.1137/s0036142994266844 · Cited by 12

Davidson method for eigenpairs and their partial derivatives of generalized eigenvalue problems

Xie, H., & Dai, H. (2005) · Communications in Numerical Methods in Engineering · doi:10.1002/cnm.811 · Cited by 12

High-Performance Passive Macromodeling Algorithms for Parallel Computing Platforms

Chinea, A., Grivet-Talocia, S., Olivadese, S. B., et al. (2013) · IEEE Transactions on Components Packaging and Manufacturing Technology · doi:10.1109/tcpmt.2013.2257193 · Cited by 12

Arnoldi versus nonsymmetric Lanczos algorithms for solving matrix eigenvalue problems

Cullum, J. K. (1996) · BIT Numerical Mathematics · doi:10.1007/bf01731928 · Cited by 12

On monotonicity of the Lanczos approximation to the matrix exponential

Druskin, V. L. (2008) · Linear Algebra and its Applications · doi:10.1016/j.laa.2008.04.046 · Cited by 12

Lateral scalability limits of silicon conduction channels

Trellakis, A., & Ravaioli, U. (1999) · Journal of Applied Physics · doi:10.1063/1.371307 · Cited by 12

Mode competition in multi-core fiber amplifier

Elkin, N. N., Napartovich, A. P., Troshchieva, V. N., et al. (2007) · Optics Communications · doi:10.1016/j.optcom.2007.05.029 · Cited by 12

A Projection Method for Optimization Problems on the Stiefel Manifold

Dalmau, O., & Oviedo, H. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-59226-8_9 · Cited by 12

Modeling the Floating Zone: Instabilities in the Half Zone and Full Zone

Houchens, B. C., & Walker, J. S. (2005) · Journal of Thermophysics and Heat Transfer · doi:10.2514/1.2178 · Cited by 12

Solving the unimolecular master equation with a weighted subspace projection method

Frankcombe, T. J., & Smith, S. C. (2000) · Journal of Computational Chemistry · doi:10.1002/(sici)1096-987x(200006)21:8 · Cited by 12

An efficient preconditioning scheme for plane-wave-based electronic structure calculations

Sawamura, A., Kohyama, M., & Keishi, T. (1999) · Computational Materials Science · doi:10.1016/s0927-0256(98)00064-0 · Cited by 12

DNS of the kappa-mechanism. I. Radial modes in the purely radiative casePreprint

Gastine, T., & Dintrans, B. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.0711.1276 · Cited by 12

Computing the Sobolev Regularity of Refinable Functions by the Arnoldi Method

Ron, A., Shen, Z., & Toh, K.-C. (2001) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479899363010 · Cited by 12

Canonical conformal variables based method for stability of Stokes waves

Dyachenko, S. A., & Semenova, A. (2022) · Studies in Applied Mathematics · doi:10.1111/sapm.12554 · Cited by 11

A non-intrusive reduced order model for the characterisation of the spatial power distribution in large thermal reactors

Abrate, N., Dulla, S., & Pedroni, N. (2023) · Annals of Nuclear Energy · doi:10.1016/j.anucene.2022.109674 · Cited by 10

Universal Features for High-Dimensional Learning and Inference

Huang, S., Makur, A., Wornell, G. W., & Zheng, L. (2024) · Foundations and Trends® in Communications and Information Theory · doi:10.1561/0100000107 · Cited by 71

Fast and scalable finite-element based approach for density functional theory calculations using projector augmented wave method

Ramakrishnan, K., Das, S. K., & Motamarri, P. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.035101 · Cited by 14

Many-body effects in the excitation spectrum of weakly interacting Bose-Einstein condensates in one-dimensional optical lattices

Beinke, R., Klaiman, S., Cederbaum, L. S., et al. (2017) · Physical Review A · doi:10.1103/physreva.95.063602 · Cited by 11

Mesh optimization to improve the stability of finite-volume methods on unstructured meshes

Zangeneh, R., & Gooch, C. F. O. (2017) · Computers & Fluids · doi:10.1016/j.compfluid.2017.04.020 · Cited by 11

Two-body Schrödinger wave functions in a plane-wave basis via separation of dimensions

Jerke, J., & Poirier, B. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5017621 · Cited by 11

Federated Principal Component Analysis for Genome-Wide Association Studies

Hartebrodt, A., Nasirigerdeh, R., Blumenthal, D. B., et al. (2021) · Proceedings · doi:10.1109/icdm51629.2021.00127 · Cited by 11

An efficient reduced‐order method for stochastic eigenvalue analysis

Zheng, Z., Beer, M., & Nackenhorst, U. (2022) · International Journal for Numerical Methods in Engineering · doi:10.1002/nme.7092 · Cited by 11

Convex Optimization for Nonequilibrium Steady States on a Hybrid Quantum Processor

Lau, J. W. Z., Lim, K. H., Bharti, K., Kwek, L. C., & Vinjanampathy, S. (2023) · Physical Review Letters · doi:10.1103/physrevlett.130.240601 · Cited by 12

Online Temperature Prediction Using a Branch Eigenmode Reduced Model Applied to Cutting Process

Videcoq, É., Lazard, M., Quéméner, O., et al. (2009) · Numerical Heat Transfer Part A Applications · doi:10.1080/10407780902821490 · Cited by 11

ZKCM: A C++ library for multiprecision matrix computation with applications in quantum information

SaiToh, A. (2013) · Computer Physics Communications · doi:10.1016/j.cpc.2013.03.022 · Cited by 11

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