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“To mitigate this bias, one strategy is to weight current sources by the norm of the EEG/MEG signals that can be generated by each of them with a unitary magnitude. Introducing this weighting to MN regularization leads to the so-called weighted minimum norm (WMN) solution (24–27).”
From Electrophysiological source imaging: A noninvasive window to brain dynamics (2018) · cites this paper as [25]
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Kolda, T. G., & Bader, B. W. (2009) · SIAM Review · doi:10.1137/07070111x · Cited by 10,624
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Moore, B. C. (1981) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1981.1102568 · Cited by 5,289
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Hansen, P. C. (1992) · SIAM Review · doi:10.1137/1034115 · Cited by 3,903
Schuck, P. (2000) · Biophysical Journal · doi:10.1016/s0006-3495(00)76713-0 · Cited by 3,868
Waldhauser, F. (2000) · Bulletin of the Seismological Society of America · doi:10.1785/0120000006 · Cited by 3,568
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Shen, Y., Harris, N. C., Skirlo, S., Prabhu, M., Baehr-Jones, T., Hochberg, M., Sun, X., Zhao, S., Larochelle, H., Englund, D., et al. (2017) · Nature Photonics · doi:10.1038/nphoton.2017.93 · Cited by 3,340
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Hansen, P. C., & O’Leary, D. P. (1993) · SIAM Journal on Scientific Computing · doi:10.1137/0914086 · Cited by 3,158
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Bro, R. (1997) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/s0169-7439(97)00032-4 · Cited by 2,824
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Bevilacqua, M., Roumy, A., Guillemot, C. M., & Morel, M.-L. A. (2012) · British Machine Vision Conference (BMVC) · doi:10.5244/c.26.135 · Cited by 3,162
Ghiorso, M. S., & Sack, R. O. (1995) · Contributions to Mineralogy and Petrology · doi:10.1007/bf00307281 · Cited by 2,782
Provencher, S. W. (1982) · Computer Physics Communications · doi:10.1016/0010-4655(82)90174-6 · Cited by 2,739
Inference of population splits and mixtures from genome-wide allele frequency data
Pickrell, J. K., & Pritchard, J. K. (2012) · PLoS Genetics · doi:10.1371/journal.pgen.1002967 · Cited by 2,731
Provencher, S. W. (1982) · Computer Physics Communications · doi:10.1016/0010-4655(82)90173-4 · Cited by 2,704
Cappellari, M., & Emsellem, É. (2004) · Publications of the Astronomical Society of the Pacific · doi:10.1086/381875 · Cited by 2,215
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Petoukhov, M. V., Franke, D., Shkumatov, A. V., Tria, G., Kikhney, A., Gajda, M. J., Gorba, C., Mertens, H. D. T., Konarev, P. V., & Svergun, D. I. (2012) · Journal of Applied Crystallography · doi:10.1107/s0021889812007662 · Cited by 1,907
Heinz, D. C., & Chein-I-Chang (2001) · IEEE Transactions on Geoscience and Remote Sensing · doi:10.1109/36.911111 · Cited by 1,860
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(1977) · Mathematics in Science and Engineering/Mathematics in science and engineering · doi:10.1016/s0076-5392(08)x6052-7 · Cited by 1,851
BIONJ: an improved version of the NJ algorithm based on a simple model of sequence data
Gascuel, O. (1997) · Molecular Biology and Evolution · doi:10.1093/oxfordjournals.molbev.a025808 · Cited by 1,850
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Lin, C. (2007) · Neural Computation · doi:10.1162/neco.2007.19.10.2756 · Cited by 1,768
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Hansen, P. C. (1994) · Numerical Algorithms · doi:10.1007/bf02149761 · Cited by 1,725
Michel, C., Murray, M. M., Lantz, G., Gonzalez, S., Spinelli, L., & de Peralta, R. G. (2004) · Clinical Neurophysiology · doi:10.1016/j.clinph.2004.06.001 · Cited by 1,771
Pedersen, J. S. (1997) · Advances in Colloid and Interface Science · doi:10.1016/s0001-8686(97)00312-6 · Cited by 1,653
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Lawson, C. L., Hanson, R. J., Kincaid, D. R., & Krogh, F. T. (1979) · ACM Transactions on Mathematical Software · doi:10.1145/355841.355847 · Cited by 1,626
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Klema, V. C., & Laub, A. J. (1980) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1980.1102314 · Cited by 1,635
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de Araújo, M. C. U., Saldanha, T. C. B., Galvão, R. K. H., Yoneyama, T., Chame, H. C., & Visani, V. (2001) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/s0169-7439(01)00119-8 · Cited by 1,332
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Rossel, R. A. V., & Behrens, T. (2010) · Geoderma · doi:10.1016/j.geoderma.2009.12.025 · Cited by 1,305
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Bardestani, R., Patience, G. S., & Kaliaguine, S. (2019) · The Canadian Journal of Chemical Engineering · doi:10.1002/cjce.23632 · Cited by 1,219
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Schittkowski, K. (1986) · Annals of Operations Research · doi:10.1007/bf02022087 · Cited by 1,157
Jaumot, J., Gargallo, R., de Juan, A., & Tauler, R. (2005) · Chemometrics and Intelligent Laboratory Systems · doi:10.1016/j.chemolab.2004.12.007 · Cited by 1,151
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Ho, L. S. T., & Ané, C. (2014) · Systematic Biology · doi:10.1093/sysbio/syu005 · Cited by 1,103
Segmentation through variable-order surface fitting
Besl, P. J., & Jain, R. (1988) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.3881 · Cited by 1,077
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Goldfarb, D., & Idnani, A. (1983) · Mathematical Programming · doi:10.1007/bf02591962 · Cited by 1,067
Hartzell, S. H., & Heaton, T. H. (1983) · Bulletin of the Seismological Society of America · doi:10.1785/bssa07306a1553 · Cited by 1,056
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Svergun, D. I., & Koch, M. H. J. (2003) · Reports on Progress in Physics · doi:10.1088/0034-4885/66/10/r05 · Cited by 1,008
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Fu, W. J. (1998) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.1998.10474784 · Cited by 1,096
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Buja, A., Hastie, T. J., & Tibshirani, R. J. (1989) · The Annals of Statistics · doi:10.1214/aos/1176347115 · Cited by 998
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Stylianou, Y., Cappé, O., & Moulines, É. (1998) · IEEE Transactions on Speech and Audio Processing · doi:10.1109/89.661472 · Cited by 933
Takane, Y., Young, F. W., & de Leeuw, J. (1977) · Psychometrika · doi:10.1007/bf02293745 · Cited by 951
DeSarbo, W. S., Benedetto, C. A. D., Song, M., & Sinha, I. (2004) · Strategic Management Journal · doi:10.1002/smj.431 · Cited by 911
Ghiorso, M. S., Hirschmann, M. M., Reiners, P. W., & Kress, V. C. (2002) · Geochemistry Geophysics Geosystems · doi:10.1029/2001gc000217 · Cited by 891
Kim, H., & Park, H. (2007) · Bioinformatics · doi:10.1093/bioinformatics/btm134 · Cited by 865
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Bro, R., & de Jong, S. (1997) · Journal of Chemometrics · doi:10.1002/(sici)1099-128x(199709/10)11:5 · Cited by 909
Jónsson, S. (2002) · Bulletin of the Seismological Society of America · doi:10.1785/0120000922 · Cited by 873
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Lowe, D. G. (1991) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.134043 · Cited by 838
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Hansen, P. C. (1987) · BIT Numerical Mathematics · doi:10.1007/bf01937276 · Cited by 830
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Pighin, F. P., Hecker, J., Lischinski, D., Szeliski, R., & Salesin, D. (2006) · ACM SIGGRAPH Conference (SIGGRAPH) · doi:10.1145/1185657.1185859 · Cited by 723
Ravikovitch, P. I., Vishnyakov, A., Russo, R., & Neimark, A. V. (2000) · Langmuir · doi:10.1021/la991011c · Cited by 707
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Gu, M., & Eisenstat, S. C. (1996) · SIAM Journal on Scientific Computing · doi:10.1137/0917055 · Cited by 700
Long, Y., Ang, K. S., Li, M., Chong, K. L. K., Sethi, R., Zhong, C., Xu, H., Ong, Z., Sachaphibulkij, K., Chen, A., et al. (2023) · Nature Communications · doi:10.1038/s41467-023-36796-3 · Cited by 700
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Ghiorso, M. S., & Carmichael, I. S. E. (1985) · Contributions to Mineralogy and Petrology · doi:10.1007/bf00378255 · Cited by 687
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Hopke, P. K. (2016) · Journal of the Air & Waste Management Association · doi:10.1080/10962247.2016.1140693 · Cited by 678
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Poole, K. T. (2005) · Cambridge University Press eBooks · doi:10.1017/cbo9780511614644 · Cited by 629
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Izvekov, S., & Voth, G. A. (2005) · The Journal of Chemical Physics · doi:10.1063/1.2038787 · Cited by 656
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Bernstein, D. S. (2005) · Cited by 632
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Lines, L. R., & Treitel, S. (1984) · Geophysical Prospecting · doi:10.1111/j.1365-2478.1984.tb00726.x · Cited by 636
Quantitative interpretation of NMR relaxation data
Whittall, K. P., & MacKay, A. L. (1989) · Journal of Magnetic Resonance (1969) · doi:10.1016/0022-2364(89)90011-5 · Cited by 633
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Field, E. H., Arrowsmith, R., Biasi, G. P., et al. (2014) · Bulletin of the Seismological Society of America · doi:10.1785/0120130164 · Cited by 633
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Ramsay, J. O., Hooker, G., Campbell, D., & Cao, J. (2007) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2007.00610.x · Cited by 613
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Tresch, M. C., Saltiel, P., & Bizzi, E. (1999) · Nature Neuroscience · doi:10.1038/5721 · Cited by 634
Lian, D., Zhao, C., Xie, X., Sun, G., Chen, E., & Rui, Y. (2014) · ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD) · doi:10.1145/2623330.2623638 · Cited by 609
Weltje, G. J. (1997) · Mathematical Geosciences · doi:10.1007/bf02775085 · Cited by 611
[8] Singular value decomposition: Application to analysis of experimental data
Henry, E. R., & Hofrichter, J. (1992) · Methods in enzymology on CD-ROM/Methods in enzymology · doi:10.1016/0076-6879(92)10010-b · Cited by 613
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Konarev, P. V., Petoukhov, M. V., Волков, В. В., & Svergun, D. I. (2006) · Journal of Applied Crystallography · doi:10.1107/s0021889806004699 · Cited by 606
Zafarani, R., Abbasi, M. A., & Liu, H. (2014) · Cambridge University Press eBooks · doi:10.1017/cbo9781139088510 · Cited by 620
Kim, H., & Park, H. (2008) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/07069239x · Cited by 574
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Atkeson, C. G., An, C. H., & Hollerbach, J. M. (1986) · The International Journal of Robotics Research · doi:10.1177/027836498600500306 · Cited by 590
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Avdeef, A. (2001) · Current Topics in Medicinal Chemistry · doi:10.2174/1568026013395100 · Cited by 595
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Gorodnitsky, I. F., George, J. S., & Rao, B. D. (1995) · Electroencephalography and Clinical Neurophysiology · doi:10.1016/0013-4694(95)00107-a · Cited by 567
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Friedrich, J. H., Zhou, P., & Paninski, L. (2017) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005423 · Cited by 533
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Paige, C. C., & Saunders, M. A. (1981) · SIAM Journal on Numerical Analysis · doi:10.1137/0718026 · Cited by 555
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Yang, J., & Leskovec, J. (2010) · Proceedings · doi:10.1109/icdm.2010.22 · Cited by 563
Metadata
- Authors
- Lawson, C. L., & Hanson, R. J.
- Affiliations
- California Institute of Technology (US)
- Venue
- Society for Industrial and Applied Mathematics eBooks
- Published
- 1995-01-01
- OpenAlex
- W2075665712
- Cited by
- 7,103
- References
- 0
- Citations by year
- 2026: 111 · 2025: 129 · 2024: 154 · 2023: 165 · 2022: 183 · 2021: 224 · 2020: 217 · 2019: 237 · 2018: 250 · 2017: 216 · 2016: 210 · 2015: 241 · 2014: 270 · 2013: 265 · 2012: 237
- FWCI
- 45.68
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Society for Industrial and Applied Mathematics eBooks (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
- Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
- Keywords
- least-squares problems, linear least squares, nonlinear least squares, numerical linear algebra, iterative methods, singular value decomposition, QR decomposition, condition number, ill-conditioned problems
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