Academic literature on the topic 'Least squares'

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Journal articles on the topic "Least squares"

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AL-CHALABI, M. "WHEN LEAST-SQUARES SQUARES LEAST1." Geophysical Prospecting 40, no. 3 (April 1992): 359–78. http://dx.doi.org/10.1111/j.1365-2478.1992.tb00380.x.

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Fearn, Tom. "Least Squares." NIR news 10, no. 1 (February 1999): 7–13. http://dx.doi.org/10.1255/nirn.502.

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Kiers, Henk A. L. "Weighted least squares fitting using ordinary least squares algorithms." Psychometrika 62, no. 2 (June 1997): 251–66. http://dx.doi.org/10.1007/bf02295279.

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Petras, Ivo, and Igor Podlubny. "Least Squares or Least Circles?" CHANCE 23, no. 2 (March 2010): 38–42. http://dx.doi.org/10.1080/09332480.2010.10739804.

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Petras, Ivo, and Igor Podlubny. "Least squares or least circles?" CHANCE 23, no. 2 (April 24, 2010): 38–42. http://dx.doi.org/10.1007/s00144-010-0021-2.

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Ward, J. "Revisiting least squares." Teaching Mathematics and its Applications 17, no. 1 (March 1, 1998): 19–21. http://dx.doi.org/10.1093/teamat/17.1.19.

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Qiu, Peihua. "Generalized Least Squares." Technometrics 47, no. 4 (November 2005): 519. http://dx.doi.org/10.1198/tech.2005.s323.

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GRANT, IAN H. W. M. "Recursive Least Squares." Teaching Statistics 9, no. 1 (January 1987): 15–18. http://dx.doi.org/10.1111/j.1467-9639.1987.tb00614.x.

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Hansen, Bruce E. "Perpendicular Least Squares." Econometric Theory 6, no. 4 (December 1990): 485. http://dx.doi.org/10.1017/s0266466600005491.

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Goerlich, Francisco. "Perpendicular Least Squares." Econometric Theory 8, no. 01 (March 1992): 147–48. http://dx.doi.org/10.1017/s0266466600010860.

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Dissertations / Theses on the topic "Least squares"

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Jones, Caroline Erin. "Least squares Gaussian quadrature." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0017/MQ54628.pdf.

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Hassel, Per Anker. "Nonlinear partial least squares." Thesis, University of Newcastle Upon Tyne, 2003. http://hdl.handle.net/10443/465.

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Partial Least Squares (PLS) has been shown to be a versatile regression technique with an increasing number of applications in the areas of process control, process monitoring and process analysis. This Thesis considers the area of nonlinear PLS; a nonlinear projection based regression technique. The nonlinearity is introduced as a univariate nonlinear function between projections, or to be more specific, linear combinations of the predictor and the response variables. As for the linear case, the method should handle multicollinearity, underdetermined and noisy systems. Although linear PLS is accepted as an empirical regression method, none of the published nonlinear PLS algorithms have achieved widespread acceptance. This is confirmed from a literature survey where few real applications of the methodology were found. This Thesis investigates two nonlinear PLS methodologies, in particular focusing on their limitations. Based on these studies, two nonlinear PLS algorithms are proposed. In the first of the two existing approaches investigated, the projections are updated by applying an optimization method to reduce the error of the nonlinear inner mapping. This ensures that the error introduced by the nonlinear inner mapping is minimized. However, the procedure is limited as a consequence of problems with the nonlinear optimisation. A new algorithm, Nested PLS (NPLS), is developed to address these issues. In particular, a separate inner PLS is used to update the projections. The NPLS algorithm is shown to outperform existing algorithms for a wide range of regression problems and has the potential to become a more widely accepted nonlinear PLS algorithm than those currently reported in the literature. In the second of the existing approaches, the projections are identified by examining each variable independently, as opposed to minimizing the error of the nonlinear inner mapping directly. Although the approach does not necessary identify the underlying functional relationship, the problems of overfitting and other problems associated with optimization are reduced. Since the underlying functional relationship may not be established accurately, the reliability of the nonlinear inner mapping will be reduced. To address this problem a new algorithm, the Reciprocal Variance PLS (RVPLS), is proposed. Compared with established methodology, RVPLS focus more on finding the underlying structure, thus reducing the difficulty of finding an appropriate inner mapping. RVPLS is shown to perform well for a number of applications, but does not have the wide-ranging performance of Nested PLS.
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Ganssle, Graham. "Stabilized Least Squares Migration." ScholarWorks@UNO, 2015. http://scholarworks.uno.edu/td/2074.

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Before raw seismic data records are interpretable by geologists, geophysicists must process these data using a technique called migration. Migration spatially repositions the acoustic energy in a seismic record to its correct location in the subsurface. Traditional migration techniques used a transpose approximation to a true acoustic propagation operator. Conventional least squares migration uses a true inverse operator, but is limited in functionality by the large size of modern seismic datasets. This research uses a new technique, called stabilized least squares migration, to correctly migrate seismic data records using a true inverse operator. Contrary to conventional least squares migration, this new technique allows for errors over ten percent in the underlying subsurface velocity model, which is a large limitation in conventional least squares migration. The stabilized least squares migration also decreases the number of iterations required by conventional least squares migration algorithms by an average of about three iterations on the sample data tested in this research.
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Young, William Ronald. "Total least squares and constrained least squares applied to frequency domain system identification." Ohio : Ohio University, 1993. http://www.ohiolink.edu/etd/view.cgi?ohiou1176315127.

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Guo, Hengdao. "Frequency Tracking and Phasor Estimation Using Least Squares and Total Least Squares Algorithms." UKnowledge, 2014. http://uknowledge.uky.edu/ece_etds/57.

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System stability plays an important role in electric power systems. With the development of electric power system, the scale of the electric grid is now becoming larger and larger, and many renewable energy resources are integrated in the grid. However, at the same time, the stability and safety issues of electric power system are becoming more complicated. Frequency and phasors are two critical parameters of the system stability. Obtaining these two parameters have been great challenges for decades. Researchers have provided various kinds of algorithms for frequency tracking and phasor estimation. Among them, Least Squares (LS) algorithm is one of the most commonly used algorithm. This thesis studies the LS algorithm and the Total Least Squares (TLS) algorithm working on frequency tracking and phasor estimation. In order to test the performance of the two algorithms, some simulations have been made in the Matlab. The Total Vector Error (TVE) is a commonly used performance criteria, and the TVE results of the two algorithms are compared. The TLS algorithm performs better than LS algorithm when the frequencies of all harmonic components are given.
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Santiago, Claudio Prata. "On the nonnegative least squares." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31768.

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Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2010.
Committee Chair: Earl Barnes; Committee Member: Arkadi Nemirovski; Committee Member: Faiz Al-Khayyal; Committee Member: Guillermo H. Goldsztein; Committee Member: Joel Sokol. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Müller, Werner. "On Least Squares Variogram Fitting." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1997. http://epub.wu.ac.at/370/1/document.pdf.

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Yao, Gang. "Least-squares reverse-time migration." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/14575.

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Conventional migration methods, including reverse-time migration (RTM) have two weaknesses: first, they use the adjoint of forward-modelling operators, and second, they usually apply a crosscorrelation imaging condition to extract images from reconstructed wavefields. Adjoint operators, which are an approximation to inverse operators, can only correctly calculate traveltimes (phase), but not amplitudes. To preserve the true amplitudes of migration images, it is necessary to apply the inverse of the forward-modelling operator. Similarly, crosscorrelation imaging conditions also only correct traveltimes (phase) but do not preserve amplitudes. Besides, the examples show crosscorrelation imaging conditions produce strong sidelobes. Least-squares migration (LSM) uses both inverse operators and deconvolution imaging conditions. As a result, LSM resolves both problems in conventional migration methods and produces images with fewer artefacts, higher resolution and more accurate amplitudes. At the same time, RTM can accurately handle all dips, frequencies and any type of velocity variation. Combining RTM and LSM produces least-squares reverse-time migration (LSRTM), which in turn has all the advantages of RTM and LSM. In this thesis, we implement two types of LSRTM: matrix-based LSRTM (MLSRTM) and non-linear LSRTM (NLLSRTM). MLSRTM is a matrix formulation of LSRTM and is more stable than conventional LSRTM; it can be implemented with linear inversion algorithms but needs a large amount of computer memory. NLLSRTM, by contrast, directly expresses migration as an optimisation which minimises the 2 norm of the residual between the predicted and observed data. NLLSRTM can be implemented using non-linear gradient inversion algorithms, such as non-linear steepest descent and non-linear conjugated-gradient solvers. We demonstrate that both MLSRTM and NLLSRTM can achieve better images with fewer artefacts, higher resolution and more accurate amplitudes than RTM using three synthetic examples. The power of LSRTM is also further illustrated using a field dataset. Finally, a simple synthetic test demonstrates that the objective function used in LSRTM is sensitive to errors in the migration velocity. As a result, it may be possible to use NLLSRTM to both refine the migrated image and estimate the migration velocity.
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Kim, Donggeon. "Least squares mixture decomposition estimation." Diss., This resource online, 1995. http://scholar.lib.vt.edu/theses/available/etd-02132009-171622/.

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Chu, Ka Lok 1975. "Inequalities and equalities associated with ordinary least squares and generalized least squares in partitioned linear models." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=85140.

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The motivation for this thesis is the paper by Paul L. Canner [The American Statistician, vol. 23, no. 5, pp. 39--40 (1969)] in which it was noted that in simple linear regression it is possible for the generalized least squares regression line to lie either entirely above or entirely below all of the observed data points.
Chapter I builds on the observation that in Canner's model the ordinary least squares and generalized least squares regression lines are parallel, which led us to introduce a new measure of efficiency of ordinary least squares and to find conditions for which the total Watson efficiency of ordinary least squares in a partitioned linear model exceeds or is less than the product of the two subset Watson efficiencies, i.e., the product of the Watson efficiencies associated with the two subsets of parameters in the underlying partitioned linear model.
We introduce the notions of generalized efficiency function, efficiency factorization multiplier, and determinantal covariance ratio, and obtain several inequalities and equalities. We give special attention to those partitioned linear models for which the total Watson efficiency of ordinary least squares equals the product of the two subset Watson efficiencies. A key characterization involves the equality between the squares of a certain partial correlation coefficient and its associated ordinary correlation coefficient.
In Chapters II and IV we suppose that the underlying partitioned linear model is weakly singular in that the column space of the model matrix is contained in the column space of the covariance matrix of the errors in the linear model. In Chapter III our results are specialized to partitioned linear models where the partitioning is orthogonal and the covariance matrix of the errors is positive definite.
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Books on the topic "Least squares"

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1938-, Hanson Richard J., ed. Solving least squares problems. Philadelphia: SIAM, 1995.

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1944-, Hilbe Joseph M., ed. Quasi-least squares regression. Boca Raton: CRC Press, Taylor & Francis Group, 2014.

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Hough, Patricia D. Stable and efficient solution of weighted least-squares problems with applications in interior point methods. Ithaca, N.Y: Cornell Theory Center, Cornell University, 1996.

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United States. National Aeronautics and Space Administration., ed. On recursive least-squares filtering algorithms and implementations. Los Angeles: University of California, 1990.

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Bartlett, Dana P. General principles of the method of least squares. Mineola, NY: Dover, 2006.

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United States. National Aeronautics and Space Administration., ed. On recursive least-squares filtering algorithms and implementations. Los Angeles: University of California, 1990.

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Latan, Hengky, and Richard Noonan, eds. Partial Least Squares Path Modeling. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-64069-3.

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Gunzburger, Max D., and Pavel B. Bochev. Least-Squares Finite Element Methods. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/b13382.

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Esposito Vinzi, Vincenzo, Wynne W. Chin, Jörg Henseler, and Huiwen Wang, eds. Handbook of Partial Least Squares. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-540-32827-8.

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Bochev, Pavel B. Least-squares finite element methods. New York: Springer, 2009.

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Book chapters on the topic "Least squares"

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Paige, Christopher C., and Zdeněk Strakoš. "Unifying Least Squares, Total Least Squares and Data Least Squares." In Total Least Squares and Errors-in-Variables Modeling, 25–34. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-017-3552-0_3.

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Lyche, Tom. "Least Squares." In Numerical Linear Algebra and Matrix Factorizations, 199–222. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36468-7_9.

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Rey Vega, Leonardo, and Hernan Rey. "Least Squares." In SpringerBriefs in Electrical and Computer Engineering, 89–112. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-30299-2_5.

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White, Halbert. "Least Squares." In Time Series and Statistics, 118–25. London: Palgrave Macmillan UK, 1990. http://dx.doi.org/10.1007/978-1-349-20865-4_15.

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Sayfy, Ali. "Least Squares." In Encyclopedia of Social Network Analysis and Mining, 1–4. New York, NY: Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4614-7163-9_149-1.

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Sen, Ashish, and Tony E. Smith. "Least Squares." In Advances in Spatial and Network Economics, 473–532. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-79880-1_7.

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Lyche, Tom, Georg Muntingh, and Øyvind Ryan. "Least Squares." In Texts in Computational Science and Engineering, 159–77. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-59789-4_9.

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Bornemann, Folkmar. "Least Squares." In Springer Undergraduate Mathematics Series, 69–74. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74222-9_4.

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Haberman, Shelby J. "Least Squares." In Springer Series in Statistics, 265–323. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4757-4417-0_5.

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Rotondi, Alberto, Paolo Pedroni, and Antonio Pievatolo. "Least Squares." In UNITEXT, 475–521. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09429-3_11.

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Conference papers on the topic "Least squares"

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Chemingui, N., F. Liu, and S. Lu. "Least-Squares Migration Beyond Primaries." In First EAGE/SBGf Workshop on Least-Squares Migration. Netherlands: EAGE Publications BV, 2018. http://dx.doi.org/10.3997/2214-4609.201803058.

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Liu, Z., and G. Schuster. "Neural Network Least Squares Migration." In First EAGE/SBGf Workshop on Least-Squares Migration. Netherlands: EAGE Publications BV, 2018. http://dx.doi.org/10.3997/2214-4609.201803061.

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Dose, V., and U. von Toussaint. "Beyond least squares." In BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: 32nd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering. AIP, 2013. http://dx.doi.org/10.1063/1.4819988.

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Karny, M. "Partitioned least squares." In International Conference on Control '94. IEE, 1994. http://dx.doi.org/10.1049/cp:19940240.

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Lunglmayr, Michael, Christoph Unterrieder, and Mario Huemer. "Approximate least squares." In ICASSP 2014 - 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2014. http://dx.doi.org/10.1109/icassp.2014.6854489.

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Qiao, Sanzheng. "Integer least squares." In the 2008 C3S2E conference. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1370256.1370261.

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Care, Algo, Simone Garatti, and Marco C. Campi. "Least squares estimates and the coverage of least squares costs." In 2013 IEEE 52nd Annual Conference on Decision and Control (CDC). IEEE, 2013. http://dx.doi.org/10.1109/cdc.2013.6760841.

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Rosset, Julien, and Laurent Donzé. "Fuzzy Least Squares and Fuzzy Orthogonal Least Squares Linear Regressions." In 15th International Conference on Fuzzy Computation Theory and Applications. SCITEPRESS - Science and Technology Publications, 2023. http://dx.doi.org/10.5220/0012182700003595.

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DaI, W., X. Cheng, K. Jiao, and D. Vigh. "Iterative Least-squares Migration without Cycle Skipping." In First EAGE/SBGf Workshop on Least-Squares Migration. Netherlands: EAGE Publications BV, 2018. http://dx.doi.org/10.3997/2214-4609.201803064.

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Piazzon, Federico, Alvise Sommariva, and Marco Vianello. "Caratheodory-Tchakaloff Least Squares." In 2017 International Conference on Sampling Theory and Applications (SampTA). IEEE, 2017. http://dx.doi.org/10.1109/sampta.2017.8024337.

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Reports on the topic "Least squares"

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Blaha, George. Nonlinear Parametric Least-Squares Adjustment. Fort Belvoir, VA: Defense Technical Information Center, March 1987. http://dx.doi.org/10.21236/ada184039.

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DREWIEN, CELESTE A. A Parallel Prediction-Augmented Classical Least Squares/Partial Least Squares Hybrid Algorithm: CPLS 1.0 Code. Office of Scientific and Technical Information (OSTI), June 2000. http://dx.doi.org/10.2172/759455.

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Li, Qin, and Les Atlas. Time-Variant Least Squares Harmonic Modeling. Fort Belvoir, VA: Defense Technical Information Center, January 2003. http://dx.doi.org/10.21236/ada436659.

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Lippert, Ross, and Ryan Rifkin. Asymptotics of Gaussian Regularized Least-Squares. Fort Belvoir, VA: Defense Technical Information Center, October 2005. http://dx.doi.org/10.21236/ada454981.

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Fraley, Christina. Algorithms for Nonlinear Least-Squares Problems. Fort Belvoir, VA: Defense Technical Information Center, May 1988. http://dx.doi.org/10.21236/ada196071.

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Wolfe, Claire M. An interactive nonlinear least squares program. Gaithersburg, MD: National Bureau of Standards, 1987. http://dx.doi.org/10.6028/nbs.tn.1238.

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Caponnetto, Andrea, and Ernesto De Vito. Fast Rates for Regularized Least-Squares Algorithm. Fort Belvoir, VA: Defense Technical Information Center, April 2005. http://dx.doi.org/10.21236/ada454989.

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Rao, Rekha R., and Peter Randall Schunk. A Galerkin least squares approach to viscoelastic flow. Office of Scientific and Technical Information (OSTI), October 2015. http://dx.doi.org/10.2172/1223166.

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Charest, Marc. Optimizing a least-squares gradient calculation for GPUs. Office of Scientific and Technical Information (OSTI), July 2022. http://dx.doi.org/10.2172/1875765.

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Zhiquiang, C., and J. Jones. Least-Squares Approaches for the Time-Dependent Maxwell Equations. Office of Scientific and Technical Information (OSTI), December 2001. http://dx.doi.org/10.2172/15002754.

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