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1

Boley, Daniel L. "Krylov space methods on state-space control models." Circuits, Systems, and Signal Processing 13, no. 6 (1994): 733–58. http://dx.doi.org/10.1007/bf02523124.

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2

Koyama, Shinsuke, Lucia Castellanos Pérez-Bolde, Cosma Rohilla Shalizi, and Robert E. Kass. "Approximate Methods for State-Space Models." Journal of the American Statistical Association 105, no. 489 (2010): 170–80. http://dx.doi.org/10.1198/jasa.2009.tm08326.

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3

Cerchi, M. "State space methods in asset pricing." Computers & Mathematics with Applications 18, no. 6-7 (1989): 581–90. http://dx.doi.org/10.1016/0898-1221(89)90109-0.

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4

Kumar, Kuldeep. "Time Series Analysis by State Space Methods." Journal of the Royal Statistical Society: Series A (Statistics in Society) 167, no. 1 (2004): 187–88. http://dx.doi.org/10.1111/j.1467-985x.2004.298_6.x.

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5

Hinich, Melvin J. "Time Series Analysis by State Space Methods." Technometrics 47, no. 3 (2005): 373. http://dx.doi.org/10.1198/tech.2005.s288.

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6

Aruoba, S. Borağan, and Sean D. Campbell. "Time Series Analysis by State-Space Methods." Journal of the American Statistical Association 98, no. 461 (2003): 255–56. http://dx.doi.org/10.1198/jasa.2003.s261.

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7

Wu, Min, Weihua Gui, and Ning Chen. "State space methods for decentralized H∞ control." Journal of Central South University of Technology 1, no. 1 (1994): 91–96. http://dx.doi.org/10.1007/bf02652093.

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8

Poncela, Pilar. "Time series analysis by state space methods." International Journal of Forecasting 20, no. 1 (2004): 139–41. http://dx.doi.org/10.1016/j.ijforecast.2003.11.005.

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9

Clements, D. J. "Rational spectral factorization using state-space methods." Systems & Control Letters 20, no. 5 (1993): 335–43. http://dx.doi.org/10.1016/0167-6911(93)90011-t.

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10

Carnerero, Panduro Alfonso Daniel, Ramirez Daniel R., Daniel Limon, and Teodoro Alamo. "Kernel-based State-Space Kriging for Predictive Control." IEEE CAA Journal of Automatica Sinica 10, no. 5 (2023): 1263–75. https://doi.org/10.1109/JAS.2023.123459.

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In this paper, we extend the State-Space Kriging (SSK) modeling technique presented in a previous work by the authors in order to consider non-autonomous systems. SSK is a data-driven method that computes predictions as linear combinations of past outputs. To model the nonlinear dynamics of the system, we propose the Kernel-based State-Space Kriging (K-SSK), a new version of the SSK where kernel functions are used instead of resorting to considerations about the locality of the data. Also, a Kalman filter can be used to improve the predictions at each time step in the case of noisy measurements. A constrained tracking Nonlinear Model Predictive Control (NMPC) scheme using the black-box input-output model obtained by means of the K-SSK prediction method is proposed. Finally, a simulation example and a real experiment are provided in order to assess the performance of the proposed controller.
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11

Proietti, Tommaso. "Temporal disaggregation by state space methods: Dynamic regression methods revisited." Econometrics Journal 9, no. 3 (2006): 357–72. http://dx.doi.org/10.1111/j.1368-423x.2006.00189.x.

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12

Bazen, Stephen, and Jean-Marie Cardebat. "Forecasting Bordeaux wine prices using state-space methods." Applied Economics 50, no. 47 (2018): 5110–21. http://dx.doi.org/10.1080/00036846.2018.1472740.

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13

Jonker, Jonathan, Aleksandr Aravkin, James V. Burke, Gianluigi Pillonetto, and Sarah Webster. "Fast robust methods for singular state-space models." Automatica 105 (July 2019): 399–405. http://dx.doi.org/10.1016/j.automatica.2019.04.015.

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14

Aksu, Celal, and Jack Y. Narayan. "Forecasting with vector ARMA and state space methods." International Journal of Forecasting 7, no. 1 (1991): 17–30. http://dx.doi.org/10.1016/0169-2070(91)90029-u.

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15

Nagy, P. A. J., and L. Ljung. "Estimating Time-Delays Via State-Space Identification Methods." IFAC Proceedings Volumes 24, no. 3 (1991): 717–20. http://dx.doi.org/10.1016/s1474-6670(17)52433-7.

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16

Parker, Simon T., David M. Lorenzetti, and Michael D. Sohn. "Implementing state-space methods for multizone contaminant transport." Building and Environment 71 (January 2014): 131–39. http://dx.doi.org/10.1016/j.buildenv.2013.09.021.

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17

EDMUNDS, J. M. "Model order determination for state-space control design methods." International Journal of Control 41, no. 4 (1985): 941–46. http://dx.doi.org/10.1080/0020718508961173.

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18

Kucera, V. "A bridge between state-space and transfer-function methods." Annual Reviews in Control 23, no. 1 (1999): 177–84. http://dx.doi.org/10.1016/s1367-5788(99)00020-6.

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19

Kučera, V. "A bridge between state-space and transfer-function methods." Annual Reviews in Control 23 (January 1999): 177–84. http://dx.doi.org/10.1016/s1367-5788(99)90085-8.

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20

Viberg, M., B. Ottersten, B. Wahlberg, and L. Ljung. "Performance of Subspace Based State-Space System Identification Methods." IFAC Proceedings Volumes 26, no. 2 (1993): 63–66. http://dx.doi.org/10.1016/s1474-6670(17)48223-1.

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21

Yiu, S. F., P. C. Young, and B. Robinson. "State-space Methods of Deconvolution for Geophysical Data Processing." IFAC Proceedings Volumes 21, no. 9 (1988): 983–87. http://dx.doi.org/10.1016/s1474-6670(17)54856-9.

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22

Hindi, K. S. "Control systems design: An introduction to state-space methods." Automatica 23, no. 6 (1987): 803–4. http://dx.doi.org/10.1016/0005-1098(87)90044-6.

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23

Pedersen, M. W., C. W. Berg, U. H. Thygesen, A. Nielsen, and H. Madsen. "Estimation methods for nonlinear state-space models in ecology." Ecological Modelling 222, no. 8 (2011): 1394–400. http://dx.doi.org/10.1016/j.ecolmodel.2011.01.007.

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24

Pakman, Ari, Jonathan Huggins, Carl Smith, and Liam Paninski. "Fast state-space methods for inferring dendritic synaptic connectivity." Journal of Computational Neuroscience 36, no. 3 (2013): 415–43. http://dx.doi.org/10.1007/s10827-013-0478-0.

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25

Arici, Yalin, and Khalid M. Mosalam. "Modal identification of bridge systems using state-space methods." Structural Control and Health Monitoring 12, no. 3-4 (2005): 381–404. http://dx.doi.org/10.1002/stc.76.

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26

Alexopoulos, Christos. "State space partitioning methods for stochastic shortest path problems." Networks 30, no. 1 (1997): 9–21. http://dx.doi.org/10.1002/(sici)1097-0037(199708)30:1<9::aid-net2>3.0.co;2-h.

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27

Zaron, Edward D. "A Comparison of Data Assimilation Methods Using a Planetary Geostrophic Model." Monthly Weather Review 134, no. 4 (2006): 1316–28. http://dx.doi.org/10.1175/mwr3124.1.

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Abstract Assimilating hydrographic observations into a planetary geostrophic model is posed as a problem in control theory. The cost functional is the sum of weighted model and data residuals. Model errors are assumed to be spatially correlated, and hydrographic station data are assimilated directly. Searches in state space and data space, for minimizing the cost functional, are compared to a direct matrix inversion algorithm in the data space. State-space methods seek the minimizer of the cost functional by performing a preconditioned search in an N-dimensional space of state or control variables, where N is approximately 650 000 in the present calculations. Data-space methods solve the Euler–Lagrange equations for the extremum of the cost functional by working in an M-dimensional dual space, where M is the number of measurements. The following four solvers are compared: (i) an iterative state-space solver, with a naive diagonal matrix preconditioner; (ii) an iterative state-space solver, with a sophisticated preconditioner based on the inverse of the model’s dynamical operators; (iii) an iterative data-space solver, with no preconditioning; and (iv) a direct, M × M matrix inversion, data-space solver. The best solver is the iterative data-space solver, (iii), which is approximately 10 times faster than the sophisticated preconditioned state-space solver, (ii), and 100 times faster than the direct data-space solver, (iv).
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28

Chukhrova, Nataliya, and Arne Johannssen. "Stochastic Claims Reserving Methods with State Space Representations: A Review." Risks 9, no. 11 (2021): 198. http://dx.doi.org/10.3390/risks9110198.

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Often, the claims reserves exceed the available equity of non-life insurance companies and a change in the claims reserves by a small percentage has a large impact on the annual accounts. Therefore, it is of vital importance for any non-life insurer to handle claims reserving appropriately. Although claims data are time series data, the majority of the proposed (stochastic) claims reserving methods is not based on time series models. Among the time series models, state space models combined with Kalman filter learning algorithms have proven to be very advantageous as they provide high flexibility in modeling and an accurate detection of the temporal dynamics of a system. Against this backdrop, this paper aims to provide a comprehensive review of stochastic claims reserving methods that have been developed and analyzed in the context of state space representations. For this purpose, relevant articles are collected and categorized, and the contents are explained in detail and subjected to a conceptual comparison.
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29

Schrempf, Andreas, and Vincent Verdult. "IDENTIFICATION OF APPROXIMATIVE NONLINEAR STATE-SPACE MODELS BY SUBSPACE METHODS." IFAC Proceedings Volumes 38, no. 1 (2005): 934–39. http://dx.doi.org/10.3182/20050703-6-cz-1902.00157.

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30

Rao, B. D. "Sensitivity considerations in state-space model-based harmonic retrieval methods." IEEE Transactions on Acoustics, Speech, and Signal Processing 37, no. 11 (1989): 1789–94. http://dx.doi.org/10.1109/29.46567.

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31

Fronk, Alexander, and Britta Kehden. "State space analysis of Petri nets with relation-algebraic methods." Journal of Symbolic Computation 44, no. 1 (2009): 15–47. http://dx.doi.org/10.1016/j.jsc.2008.04.005.

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32

Rachid, Mansouri, Bettayeb Maamar, and Djennoune Said. "Comparison between two approximation methods of state space fractional systems." Signal Processing 91, no. 3 (2011): 461–69. http://dx.doi.org/10.1016/j.sigpro.2010.03.006.

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33

Liu, Chao-Lin, and Michael P. Wellman. "Evaluation of Bayesian networks with flexible state-space abstraction methods." International Journal of Approximate Reasoning 30, no. 1 (2002): 1–39. http://dx.doi.org/10.1016/s0888-613x(01)00067-6.

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34

Doucet, Arnaud, and Vladislav B. Tadić. "Parameter estimation in general state-space models using particle methods." Annals of the Institute of Statistical Mathematics 55, no. 2 (2003): 409–22. http://dx.doi.org/10.1007/bf02530508.

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35

Kantas, Nikolas, Arnaud Doucet, Sumeetpal S. Singh, Jan Maciejowski, and Nicolas Chopin. "On Particle Methods for Parameter Estimation in State-Space Models." Statistical Science 30, no. 3 (2015): 328–51. http://dx.doi.org/10.1214/14-sts511.

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36

Boukraa, S., and J. ‐L Basdevant. "Technical methods for solving bound‐state equations in momentum space." Journal of Mathematical Physics 30, no. 5 (1989): 1060–72. http://dx.doi.org/10.1063/1.528376.

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37

Parker, S. T., and V. Bowman. "State-space methods for calculating concentration dynamics in multizone buildings." Building and Environment 46, no. 8 (2011): 1567–77. http://dx.doi.org/10.1016/j.buildenv.2011.01.016.

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38

Sanderson, P. M., A. G. Verhage, and R. B. Fuld. "State-space and verbal protocol methods for studying the human." Applied Ergonomics 22, no. 1 (1991): 60. http://dx.doi.org/10.1016/0003-6870(91)90025-d.

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39

Leeser, Miriam, and Valerie Ohm. "Accurate Power Estimation for Sequential CMOS Circuits Using Graph-based Methods." VLSI Design 12, no. 2 (2001): 187–203. http://dx.doi.org/10.1155/2001/73872.

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We present a novel method for estimating the power of sequential CMOS circuits. Symbolic probabilistic power estimation with an enumerated state space is used to estimate the average power switched by the circuit. This approach is more accurate than simulation based methods. Automatic circuit partitioning and state space exploration provide improvements in run-time and storage requirements over existing approaches. Circuits are automatically partitioned to improve the execution time and to allow larger circuits to be processed. Spatial correlation is dealt with by minimizing the cutset between partitions which tends to keep areas of reconvergent fanout in the same partition. Circuit partitions can be recombined using our combinational estimation methods which allow the exploitation of knowledge of probabilities of the circuit inputs. We enumerate the state transition graph (STG) incrementally using state space exploration methods developed for formal verification. Portions of the STG are generated on an as-needed basis, and thrown away after they are processed. BDDs are used to compactly represent similar states. This saves significant space in the storage of the STG. Our results show that modeling the state space is imperative for accurate power estimation of sequential circuits, partitioning saves time, and incremental state space exploration saves storage space. This allows us to process larger circuits than would otherwise be possible
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40

Kim, Seong-Eun, Michael K. Behr, Demba Ba, and Emery N. Brown. "State-space multitaper time-frequency analysis." Proceedings of the National Academy of Sciences 115, no. 1 (2017): E5—E14. http://dx.doi.org/10.1073/pnas.1702877115.

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Time series are an important data class that includes recordings ranging from radio emissions, seismic activity, global positioning data, and stock prices to EEG measurements, vital signs, and voice recordings. Rapid growth in sensor and recording technologies is increasing the production of time series data and the importance of rapid, accurate analyses. Time series data are commonly analyzed using time-varying spectral methods to characterize their nonstationary and often oscillatory structure. Current methods provide local estimates of data features. However, they do not offer a statistical inference framework that applies to the entire time series. The important advances that we report are state-space multitaper (SS-MT) methods, which provide a statistical inference framework for time-varying spectral analysis of nonstationary time series. We model nonstationary time series as a sequence of second-order stationary Gaussian processes defined on nonoverlapping intervals. We use a frequency-domain random-walk model to relate the spectral representations of the Gaussian processes across intervals. The SS-MT algorithm efficiently computes spectral updates using parallel 1D complex Kalman filters. An expectation–maximization algorithm computes static and dynamic model parameter estimates. We test the framework in time-varying spectral analyses of simulated time series and EEG recordings from patients receiving general anesthesia. Relative to standard multitaper (MT), SS-MT gave enhanced spectral resolution and noise reduction (&gt;10 dB) and allowed statistical comparisons of spectral properties among arbitrary time series segments. SS-MT also extracts time-domain estimates of signal components. The SS-MT paradigm is a broadly applicable, empirical Bayes’ framework for statistical inference that can help ensure accurate, reproducible findings from nonstationary time series analyses.
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41

LEDEZMA, AGAPITO, RICARDO ALER, and DANIEL BORRAJO. "EXPLORING THE STACKING STATE-SPACE." International Journal on Artificial Intelligence Tools 11, no. 02 (2002): 267–82. http://dx.doi.org/10.1142/s0218213002000897.

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Nowadays, there is no doubt that machine learning techniques can be successfully applied to data mining tasks. Currently, the combination of several classifiers is one of the most active fields within inductive machine learning. Examples of such techniques are boosting, bagging and stacking. From these three techniques, stacking is perhaps the less used one. One of the main reasons for this relates to the difficulty to define and parameterize its components: selecting which combination of base classifiers to use, and which classifier to use as the meta-classifier. One could use for that purpose simple search methods (e.g. hill climbing), or more complex ones (e.g. genetic algorithms). But before search is attempted, it is important to know the properties of the search space itself. In this paper we study exhaustively the space of Stacking systems that can be built by using four base learning systems: C4.5, IB1, Naive Bayes, and PART. We have also used the Multiple Linear Response (MLR) as meta-classifier. The properties of this state-space obtained in this paper will be useful for designing new Stacking-based algorithms and tools.
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42

Hemami, H., and M. Hemami. "State Space Methods and Examples for Computational Models of Human Movement." Mechanical Engineering Research 6, no. 1 (2016): 46. http://dx.doi.org/10.5539/mer.v6n1p46.

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&lt;p&gt;In the past, multi-rigid-body systems have been formulated by Lagrangian and Hamiltonian dynamics, the Newton-Euler method and Kane’s dynamic equations. Availability of large computers and versatile software systems enables us to formulate larger systems and analyze them computationally. In such circumstances, the probability of human error grows with the size of the system. The purpose of this work is to provide state space formulations that allow verification of computational results and be able to transport Lyapunov stability results across the these dynamics disciplines. The formulations are presented with matrices for all transformations and projections.&lt;/p&gt;&lt;p&gt;This work also investigates the constraint forces and their computation or elimination by different methods. A one-link constrained rigid body is considered first. The results are summarily extended to a three-link system. Six three-link rigid body sub modules are interconnected to describe, control and simulate many different maneuvers and activities of humans.&lt;/p&gt;&lt;p&gt;The actuators have alpha and gamma inputs, and pull but cannot push. The control strategy is based on Evarts’ “attention set,”, and is applied to the movement of one arm in a computational experiment.&lt;/p&gt;
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43

IIMA, Hitoshi, and Yasuaki KUROE. "Swarm Reinforcement Learning Methods for Problems with Continuous State-action Space." Transactions of the Society of Instrument and Control Engineers 48, no. 11 (2012): 790–98. http://dx.doi.org/10.9746/sicetr.48.790.

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44

Cedeño, Angel L., Ricardo Albornoz, Rodrigo Carvajal, Boris I. Godoy, and Juan C. Agüero. "On Filtering Methods for State-Space Systems having Binary Output Measurements." IFAC-PapersOnLine 54, no. 7 (2021): 815–20. http://dx.doi.org/10.1016/j.ifacol.2021.08.462.

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45

Subrahmanyam, M. B. "Synthesis of finite-interval H(infinity) controllers by state-space methods." Journal of Guidance, Control, and Dynamics 13, no. 4 (1990): 624–29. http://dx.doi.org/10.2514/3.25379.

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46

Garcia-Hiernaux, Alfredo, José Casals, and Miguel Jerez. "Fast estimation methods for time-series models in state–space form." Journal of Statistical Computation and Simulation 79, no. 2 (2009): 121–34. http://dx.doi.org/10.1080/00949650701617249.

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47

Wellstead, P. E. "Book Review: Control System Design—An Introduction to State Space Methods." International Journal of Electrical Engineering & Education 23, no. 4 (1986): 380. http://dx.doi.org/10.1177/002072098602300437.

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48

Duri, S., U. Buy, R. Devarapalli, and S. M. Shatz. "Using state space reduction methods for deadlock analysis in Ada tasking." ACM SIGSOFT Software Engineering Notes 18, no. 3 (1993): 51–60. http://dx.doi.org/10.1145/174146.154197.

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49

Hostetter, G. "Book reviews - Control system design: An introduction to state-space methods." IEEE Control Systems Magazine 6, no. 5 (1986): 55. http://dx.doi.org/10.1109/mcs.1986.1105120.

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50

Cummins, Bree, Tomáš Gedeon, and Kelly Spendlove. "On the Efficacy of State Space Reconstruction Methods in Determining Causality." SIAM Journal on Applied Dynamical Systems 14, no. 1 (2015): 335–81. http://dx.doi.org/10.1137/130946344.

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