The DOI matches its Crossref record.
Numerical Linear Algebra
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“For a backward-stable evaluation, the standard perturbation bound of numerical linear algebra [32,33] gives a relative forward error”
From Curvature-Corrected Rotary Position Embeddings: An Entropy-Invariant Temperature for Mitigating Numerical-Rank Collapse in Long-Context Attention (2026) · cites this paper as [33]
Citations
Cited by
Sorted by citations
Items 301–400 of 1,001
Radial basis function approximation methods with extended precision floating point arithmetic
Sarra, S. A. (2010) · Engineering Analysis with Boundary Elements · doi:10.1016/j.enganabound.2010.05.011 · Cited by 56
Multiple resolution surface wave tomography: the Mediterranean basin
Boschi, L., Ekström, G., & Kustowski, B. (2004) · Geophysical Journal International · doi:10.1111/j.1365-246x.2004.02194.x · Cited by 56
Robust Matrix Completion via Alternating Projection
Jiang, X., Zhong, Z., Liu, X., & So, H. C. (2017) · IEEE Signal Processing Letters · doi:10.1109/lsp.2017.2685518 · Cited by 55
Distributed Averaging and Balancing in Network Systems
Hadjicostis, C. N., Domínguez-García, A. D., & Charalambous, T. (2018) · Foundations and Trends® in Systems and Control · doi:10.1561/2600000016 · Cited by 55
Trefethen, L. N. (1999) · Springer series in computational mathematics · doi:10.1007/978-3-662-03972-4_6 · Cited by 56
Self-citationInverse barotropic tidal estimation for regional ocean applications
Logutov, O. G., & Lermusiaux, P. F. J. (2008) · Ocean Modelling · doi:10.1016/j.ocemod.2008.06.004 · Cited by 56
How many shuffles to randomize a deck of cards?
Trefethen, L. N., & Trefethen, L. M. (2000) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2000.0625 · Cited by 55
Self-citationNormalized LMS algorithm and data-selective strategies for adaptive graph signal estimation
Spelta, M. J. M., & Martins, W. A. (2019) · Signal Processing · doi:10.1016/j.sigpro.2019.107326 · Cited by 55
Viola, F., Spandan, V., Meschini, V., et al. (2021) · Computer Physics Communications · doi:10.1016/j.cpc.2021.108248 · Cited by 55
Minimizing Delay for Multicast-Streaming in Wireless Networks with Network Coding
Yeow, W.-L., Hoang, A. T., & Tham, C. (2009) · IEEE Conference on Computer Communications (INFOCOM) · doi:10.1109/infcom.2009.5061921 · Cited by 55
An Improved Algorithm for the Solution of the Regularization Path of Support Vector Machine
Ong, C., Shao, S., & Yang, J. (2010) · IEEE Transactions on Neural Networks · doi:10.1109/tnn.2009.2039000 · Cited by 55
Compact signatures for high-speed interest point description and matching
Calonder, M., Lepetit, V., Fua, P., Konolige, K., Bowman, J., & Mihelich, P. (2009) · IEEE/CVF International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2009.5459272 · Cited by 55
Multi-resolution Dynamic Mode Decomposition for Foreground/Background Separation and Object Tracking
Kutz, J. N., Fu, X., Brunton, S. L., et al. (2015) · doi:10.1109/iccvw.2015.122 · Cited by 55
Deep learning for in situ data compression of large turbulent flow simulations
Glaws, A., King, R., & Sprague, M. (2020) · Physical Review Fluids · doi:10.1103/physrevfluids.5.114602 · Cited by 53
The critical layer in pipe flow at high Reynolds number
Viswanath, D. (2008) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2008.0225 · Cited by 55
Fast Estimation of Multinomial Logit Models: R Package mnlogit
Hasan, A., Wang, Z., & Mahani, A. S. (2016) · Journal of Statistical Software · doi:10.18637/jss.v075.i03 · Cited by 54
Hermitian zero modes protected by nonnormality: Application of pseudospectra
Ōkuma, N., & Sato, M. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.102.014203 · Cited by 53
Efficient spatially resolved multimode quantum memory
Surmacz, K., Nunn, J., Reim, K., et al. (2008) · Physical Review A · doi:10.1103/physreva.78.033806 · Cited by 54
Intraband absorption and Stark effect in silicon nanocrystals
de Sousa, J. S., Leburton, J., Freire, V. N., et al. (2005) · Physical Review B · doi:10.1103/physrevb.72.155438 · Cited by 54
Flight Results of Vision-Based Navigation for Autonomous Spacecraft Inspection of Unknown Objects
Fourie, D., Tweddle, B. E., Ulrich, S., et al. (2014) · Journal of Spacecraft and Rockets · doi:10.2514/1.a32813 · Cited by 54
On the singular values of Gaussian random matrices
Shen, J. (2001) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(00)00322-0 · Cited by 54
On Solving Optimization Problems with Hidden Nonconvex Structures
Strekalovsky, A. S. (2014) · Springer eBooks · doi:10.1007/978-1-4939-0808-0_23 · Cited by 54
Efficient and Non-Convex Coordinate Descent for Symmetric Nonnegative Matrix Factorization
Vandaele, A., Gillis, N., Lei, Q., et al. (2016) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2016.2591510 · Cited by 54
Zhang, Y., Kurata, M., & Lynch, J. P. (2016) · Journal of Engineering Mechanics · doi:10.1061/(asce)em.1943-7889.0001198 · Cited by 55
Hydrodynamic flows on curved surfaces: Spectral numerical methods for radial manifold shapes
Gross, B. J., & Atzberger, P. J. (2018) · Journal of Computational Physics · doi:10.1016/j.jcp.2018.06.013 · Cited by 51
Vu, V. (2008) · Bolyai Society mathematical studies · doi:10.1007/978-3-540-77200-2_13 · Cited by 53
Qin, W. B., & Orosz, G. (2017) · Transportation Research Part C Emerging Technologies · doi:10.1016/j.trc.2017.07.005 · Cited by 53
Accurate computation of the Moore–Penrose inverse of strictly totally positive matrices
Marco, A., & Martínez, J. (2018) · Journal of Computational and Applied Mathematics · doi:10.1016/j.cam.2018.10.009 · Cited by 53
The Laplacian Paradigm: Emerging Algorithms for Massive Graphs
Teng, S. (2010) · Lecture notes in computer science · doi:10.1007/978-3-642-13562-0_2 · Cited by 49
An Arnoldi approach for generation of reduced-order models for turbomachinery
Willcox, K. E., Peraire, J., & White, J. K. (2002) · Computers & Fluids · doi:10.1016/s0045-7930(01)00046-9 · Cited by 53
Design and Analysis of Longitudinal Controller for the Platoon With Time-Varying Delay
Huang, D., Li, S., Zhang, Z., et al. (2022) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2022.3200026 · Cited by 52
Model-reduced gradient-based history matching
Kaleta, M. P., Hanea, R. G., Heemink, A. W., & Jansen, J.-D. D. (2010) · Computational Geosciences · doi:10.1007/s10596-010-9203-5 · Cited by 54
Parvaix, M., & Girin, L. (2010) · IEEE Transactions on Audio Speech and Language Processing · doi:10.1109/tasl.2010.2097250 · Cited by 52
Harmonic and Interharmonic Phasor Estimation Using Matrix Pencil Method for Phasor Measurement Units
Bernard, L., Goondram, S., Bahrani, B., et al. (2020) · IEEE Sensors Journal · doi:10.1109/jsen.2020.3009643 · Cited by 52
Fundamental Limits to Near-Field Optical Response over Any Bandwidth
Shim, H., Fan, L., Johnson, S. G., & Miller, O. D. (2019) · Physical Review X · doi:10.1103/physrevx.9.011043 · Cited by 55
Mechali, O., Xu, L., Xie, X., et al. (2022) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2022.01.010 · Cited by 51
SVD perspectives for augmenting DeepONet flexibility and interpretability
Venturi, S., & Casey, T. A. (2022) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2022.115718 · Cited by 67
Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse
Rump, S. M. (2010) · BIT Numerical Mathematics · doi:10.1007/s10543-010-0294-0 · Cited by 51
Lehmann, D. J., & Theisel, H. (2013) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2013.182 · Cited by 51
Isogeometric Schwarz preconditioners for linear elasticity systems
da Veiga, L. B., Cho, D., Pavarino, L. F., et al. (2012) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2012.10.011 · Cited by 51
Shevtsova, V. M., Sechenyh, V. V., NEPOMNYASHCHY, A. A., et al. (2011) · The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics · doi:10.1080/14786435.2011.586376 · Cited by 51
Direct multichannel predictive deconvolution
Porsani, M. J., & Ursin, B. (2007) · Geophysics · doi:10.1190/1.2432260 · Cited by 51
Limits to the Optical Response of Graphene and Two-Dimensional Materials
Miller, O. D., Ilic, O., Christensen, T., Reid, M. T. H., Atwater, H. A., Joannopoulos, J. D., Marin Soljacic, A., & Johnson, S. G. (2017) · Nano Letters · doi:10.1021/acs.nanolett.7b02007 · Cited by 51
Rodgers, C. T., & Robson, M. D. (2015) · Magnetic Resonance in Medicine · doi:10.1002/mrm.25618 · Cited by 51
Choi, S.-C. T., & Saunders, M. A. (2014) · ACM Transactions on Mathematical Software · doi:10.1145/2527267 · Cited by 51
The European Upper Mantle as Seen by Surface Waves
Boschi, L., Fry, B., Ekström, G., & Giardini, D. (2009) · Surveys in Geophysics · doi:10.1007/s10712-009-9066-2 · Cited by 51
Double Preconditioning for Gabor Frames
Balázs, P., Feichtinger, H. G., Hampejs, M., et al. (2006) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2006.882100 · Cited by 51
The Cost-Accuracy Trade-Off in Operator Learning with Neural Networks
de Hoop, M. V., Huang, D. Z., Qian, E., & Stuart, A. M. (2022) · Journal of Machine Learning · doi:10.4208/jml.220509 · Cited by 100
Mechanical design, modelling and control of a novel aerial manipulator
Nikou, A., Gavridis, G. C., & Kyriakopoulos, K. J. (2015) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra.2015.7139851 · Cited by 50
On decentralized connectivity maintenance for mobile robotic systems
Sabattini, L., Chopra, N., & Secchi, C. (2011) · doi:10.1109/cdc.2011.6161067 · Cited by 50
van Haasteren, R., & Vallisneri, M. (2014) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stu2157 · Cited by 50
Haidar, A., Ltaief, H., & Dongarra, J. J. (2011) · doi:10.1145/2063384.2063394 · Cited by 50
Łuszczek, P., Ltaief, H., & Dongarra, J. J. (2011) · Proceedings - IEEE International Parallel and Distributed Processing Symposium · doi:10.1109/ipdps.2011.91 · Cited by 50
Climate sensitivities via a Fokker–Planck adjoint approach
Thuburn, J. (2005) · Quarterly Journal of the Royal Meteorological Society · doi:10.1256/qj.04.46 · Cited by 48
Reconstruction of basal properties in ice sheets using iterative inverse methods
Habermann, M., Maxwell, D., & Truffer, M. (2012) · Journal of Glaciology · doi:10.3189/2012jog11j168 · Cited by 48
Batched QR and SVD algorithms on GPUs with applications in hierarchical matrix compression
Boukaram, W., Turkiyyah, G. M., Ltaief, H., et al. (2017) · Parallel Computing · doi:10.1016/j.parco.2017.09.001 · Cited by 50
Wen, F., Zhang, Z., & Zhang, G. (2019) · IEEE Access · doi:10.1109/access.2019.2912842 · Cited by 49
A fast multipole method for the Rotne–Prager–Yamakawa tensor and its applications
Liang, Z., Gimbutas, Z., Greengard, L., et al. (2012) · Journal of Computational Physics · doi:10.1016/j.jcp.2012.09.021 · Cited by 49
Further Complexity Reduction Using Rotational Symmetry for EDAS in Spatial Modulation
Wang, N., Liu, W., Men, H., et al. (2014) · IEEE Communications Letters · doi:10.1109/lcomm.2014.2347954 · Cited by 49
Biomolecular electrostatics—I want your solvation (model)
Bardhan, J. P. (2012) · Computational Science & Discovery · doi:10.1088/1749-4699/5/1/013001 · Cited by 49
LowCon: A Design-based Subsampling Approach in a Misspecified Linear Model
Meng, C., Xie, R., Mandal, A., et al. (2020) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.2020.1844215 · Cited by 49
Inversion of k -tridiagonal matrices with Toeplitz structure
Jia, J.-T., Sogabe, T., & El-Mikkawy, M. E. A. (2012) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2012.11.001 · Cited by 48
Preserving multiple first integrals by discrete gradients
Dahlby, M., Owren, B., & Yaguchi, T. (2011) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/44/30/305205 · Cited by 48
Lossless image compression with projection-based and adaptive reversible integer wavelet transforms
Deever, A. T., & Hemami, S. S. (2003) · IEEE Transactions on Image Processing · doi:10.1109/tip.2003.812374 · Cited by 48
Joint compensation of IQ imbalance and phase noise in OFDM wireless systems
Zou, Q., Tarighat, A., & Sayed, A. H. (2009) · IEEE Transactions on Communications · doi:10.1109/tcomm.2009.02.060526 · Cited by 48
IDENTIFYING IMPORTANT CLASSES OF LARGE SOFTWARE SYSTEMS THROUGH K-CORE DECOMPOSITION
MEYER, P., Siy, H. P., & Bhowmick, S. (2014) · Advances in Complex Systems · doi:10.1142/s0219525915500046 · Cited by 48
Contact problem for elastic spheres: Applicability of the Hertz theory to non-small contact areas
Zhupanska, O. I. (2011) · International Journal of Engineering Science · doi:10.1016/j.ijengsci.2011.02.003 · Cited by 49
Reconstruction of blade tip-timing signals based on the MUSIC algorithm
Liu, Z., Duan, F., Niu, G., et al. (2021) · Mechanical Systems and Signal Processing · doi:10.1016/j.ymssp.2021.108137 · Cited by 47
A Time-Domain Least Squares Approach to Electrochemical Impedance Spectroscopy
Lindahl, P. A., Cornachione, M., & Shaw, S. R. (2012) · IEEE Transactions on Instrumentation and Measurement · doi:10.1109/tim.2012.2210457 · Cited by 48
Computing periodic orbits with arbitrary precision
Abad, A., Barrio, R., & Dena, Á. (2011) · Physical Review E · doi:10.1103/physreve.84.016701 · Cited by 47
Graph partitioning and disturbed diffusion
Meyerhenke, H., Monien, B., & Schamberger, S. (2009) · Parallel Computing · doi:10.1016/j.parco.2009.09.006 · Cited by 47
Compressed sensing and Cholesky decomposition on FPGAs and GPUs
Yang, D., Peterson, G. D., & Li, H. (2012) · Parallel Computing · doi:10.1016/j.parco.2012.03.001 · Cited by 47
Vlasov, A. N., Antonsen, T. M., Chernyavskiy, I. A., et al. (2012) · IEEE Transactions on Plasma Science · doi:10.1109/tps.2012.2188547 · Cited by 47
Temporal and null‐space filter for the material point method
Tran, Q. A., & Sołowski, W. T. (2019) · International Journal for Numerical Methods in Engineering · doi:10.1002/nme.6138 · Cited by 47
A fixed-point implementation of matrix inversion using Cholesky decomposition
Burian, A., Takala, J., & Ylinen, M. (2006) · doi:10.1109/mwscas.2003.1562564 · Cited by 47
Low-dimensional, morphologically accurate models of subthreshold membrane potential
Kellems, A. R., Roos, D., Xiao, N., & Cox, S. J. (2009) · Journal of Computational Neuroscience · doi:10.1007/s10827-008-0134-2 · Cited by 49
Householder triangularization of a quasimatrix
Trefethen, L. N. (2009) · IMA Journal of Numerical Analysis · doi:10.1093/imanum/drp018 · Cited by 47
Self-citationElectromagnetic induction in a generalized 3D anisotropic earth, Part 2: The LIN preconditioner
Weiss, C. J., & Newman, G. A. (2003) · Geophysics · doi:10.1190/1.1581044 · Cited by 47
Molecular State Reconstruction by Nonlinear Wave Packet Interferometry
Humble, T. S., & Cina, J. A. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.060402 · Cited by 47
Efficient Detectors for Joint Compressed Sensing Detection and Channel Decoding
Schepker, H., Bockelmann, C., & Dekorsy, A. (2015) · IEEE Transactions on Communications · doi:10.1109/tcomm.2015.2424414 · Cited by 46
Clainche, S. L., Li, J. I., Theofilis, V., et al. (2014) · Aerospace Science and Technology · doi:10.1016/j.ast.2014.03.017 · Cited by 46
The ERBlet transform: An auditory-based time-frequency representation with perfect reconstruction
Necciari, T., Balázs, P., Holighaus, N., et al. (2013) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp.2013.6637697 · Cited by 46
Sainath, K., Teixeira, F. L., & Donderici, B. (2014) · Physical Review E · doi:10.1103/physreve.89.013312 · Cited by 46
Fast Spectral Ranking for Similarity Search
İşcen, A., Avrithis, Y., Tolias, G., Furon, T., & Chum, O. (2018) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2018.00796 · Cited by 49
Markov Chains With Maximum Entropy for Robotic Surveillance
George, M., Jafarpour, S., & Bullo, F. (2018) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2018.2844120 · Cited by 46
A Dynamic Mode Decomposition Approach With Hankel Blocks to Forecast Multi-Channel Temporal Series
Filho, Ê. V., & dos Santos, P. L. (2019) · IEEE Control Systems Letters · doi:10.1109/lcsys.2019.2917811 · Cited by 46
Lee, H.-J., Chu, C., & Feng, W. (2004) · Linear Algebra and its Applications · doi:10.1016/j.laa.2004.10.011 · Cited by 46
Model Selection and Mixed-Effects Modeling of HIV Infection Dynamics
Bortz, D. M., & Nelson, P. W. (2006) · Bulletin of Mathematical Biology · doi:10.1007/s11538-006-9084-x · Cited by 46
Articulated mechanism design with a degree of freedom constraint
Kawamoto, A., Bendsøe, M. P., & Sigmund, O. (2004) · International Journal for Numerical Methods in Engineering · doi:10.1002/nme.1119 · Cited by 46
Read, A. P., Chapman, B. J., Lei, C. U., et al. (2023) · Physical Review Applied · doi:10.1103/physrevapplied.19.034064 · Cited by 45
Spatial covariance modelling in a complex coastal domain by multidimensional scaling
Løland, A., & Høst, G. (2003) · Environmetrics · doi:10.1002/env.588 · Cited by 45
Weber, I. G., Ukkonen, A., & Gionis, A. (2012) · ACM International Conference on Web Search and Data Mining (WSDM) · doi:10.1145/2124295.2124369 · Cited by 45
A GCV based Arnoldi-Tikhonov regularization method
Novati, P., & Russo, M. R. (2013) · BIT Numerical Mathematics · doi:10.1007/s10543-013-0447-z · Cited by 45
A Sparse Matrix Personality for the Convey HC-1
Nagar, K. K., & Bakos, J. D. (2011) · IEEE International Symposium on Field-Programmable Custom Computing Machines (FCCM) · doi:10.1109/fccm.2011.60 · Cited by 45
Baroudi, D., Ferrantelli, A., Li, K. Y., et al. (2017) · Combustion and Flame · doi:10.1016/j.combustflame.2017.04.017 · Cited by 45
Verdugo, F., & Wall, W. A. (2016) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2016.07.016 · Cited by 45
Planar methods and grossone for the Conjugate Gradient breakdown in nonlinear programming
Leone, R. D., Fasano, G., & Sergeyev, Y. D. (2017) · Computational Optimization and Applications · doi:10.1007/s10589-017-9957-y · Cited by 45
Eigenvalue computation in the 20th century
Golub, G. H., & van der Vorst, H. A. (2001) · Elsevier eBooks · doi:10.1016/b978-0-444-50617-7.50010-0 · Cited by 45
A Krylov–Schur approach to the truncated SVD
Stoll, M. (2011) · Linear Algebra and its Applications · doi:10.1016/j.laa.2011.07.022 · Cited by 45
On the continuum limit of a discrete inverse spectral problem on optimal finite difference grids
Borcea, L., Druskin, V. L., & Knizhnerman, L. A. (2005) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.20073 · Cited by 45
Metadata
- Authors
- Trefethen, L. N., & Bau, III
- Affiliations
- University of Oxford (GB)
- Microsoft Corporation
- ORCID
- Trefethen, Lloyd N.
- Venue
- Society for Industrial and Applied Mathematics eBooks
- Published
- 1997-01
- OpenAlex
- W4320800818
- Cited by
- 3,301
- References
- 0
- Citations by year
- 2026: 97 · 2025: 179 · 2024: 148 · 2023: 192 · 2022: 194 · 2021: 186 · 2020: 209 · 2019: 174 · 2018: 179 · 2017: 169 · 2016: 145 · 2015: 150 · 2014: 176 · 2013: 164 · 2012: 150
- FWCI
- 5.17
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Society for Industrial and Applied Mathematics eBooks (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Numerical Methods and Algorithms
- Physical Sciences › Mathematics › Modeling and Simulation › Mathematical and Computational Methods
- Keywords
- numerical linear algebra, linear systems, eigenvalue problem, singular value decomposition, least squares, QR decomposition, LU decomposition, Cholesky decomposition, iterative methods
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review