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1

Vidyasagar, M. Control system synthesis: A factorization approach. San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA): Morgan & Claypool, 2011.

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2

Control system synthesis: A factorization approach. Cambridge, Mass: MIT Press, 1985.

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3

Gohberg, Israel, Nenad Manojlovic, and António Ferreira dos Santos, eds. Factorization and Integrable Systems. Basel: Birkhäuser Basel, 2003. http://dx.doi.org/10.1007/978-3-0348-8003-9.

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4

Naik, Vijay K. Data traffic reduction schemes for Cholesky factorization on asynchronous multiprocessor systems. Hampton, Va: ICASE, 1989.

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5

Symeonidis, Panagiotis, and Andreas Zioupos. Matrix and Tensor Factorization Techniques for Recommender Systems. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-41357-0.

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6

Jonathan, Wu Q. M., ed. Guide to three dimensional structure and motion factorization. London: Springer, 2011.

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7

Rothberg, Edward. Improved load distribution in parallel sparse Cholesky factorization. [Moffett Field, Calif.]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1994.

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8

1928-, Gohberg I., Manojlovic Nenad 1962-, and Santos, António Ferreira dos, 1939-, eds. Factorization and integrable systems: Summer school in Faro, Portugal, September 2000. Boston: Birkhäuser, 2003.

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9

Gohberg, Israel. Factorization and Integrable Systems: Summer School in Faro, Portugal, September 2000. Basel: Birkhäuser Basel, 2003.

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10

Burns, John A. Factorization and reduction methods for optimal control of distributed parameter systems. Hampton, Va: ICASE, 1985.

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11

Spectral theory of canonical differential systems: Method of operator identities. Basel: Birkhäuser Verlag, 1999.

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12

Loan, Charles F. Van. A block QR factorization scheme for loosely coupled systems of array processors. Ithaca, N.Y: Cornell Theory Center, Cornell University, 1987.

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13

Razavi, H. C. Fault-tolerant control of large space structures using the stable factorization approach. Cambridge, Mass: Scientific Systems, 1986.

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14

K, Mehra R., Vidyasagar M. 1947-, and United States. National Aeronautics and Space Administration. Scientific and Technical Information Branch., eds. Fault-tolerant control of large space structures using the stable factorization approach. [Washington, D.C.]: National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1986.

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15

K, Mehra R., Vidyasagar M. 1947-, and United States. National Aeronautics and Space Administration. Scientific and Technical Information Branch., eds. Fault-tolerant control of large space structures using the stable factorization approach. [Washington, D.C.]: National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1986.

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16

B, King Belinda, and Institute for Computer Applications in Science and Engineering., eds. A note on the mathematical modelling of damped second order systems. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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17

Solving linear systems: An analysis of matrix prefactorization iterative methods. Ithaca, NY: Matrix Editions, 2009.

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18

F, Knight Norman, Davis D. Dale, United States. Army Aviation Research and Technology Activity., and Langley Research Center, eds. High-performance equation solvers and their impact on finite element analysis. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1990.

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19

Center, Langley Research, ed. Multi-color incomplete Cholesky conjugate gradient methods for vector computers. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1986.

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20

Koli︠a︡da, S. F. Dynamics and numbers: A special program, June 1-July 31, 2014, Max Planck Institute for Mathematics, Bonn, Germany : international conference, July 21-25, 2014, Max Planck Institute for Mathematics, Bonn, Germany. Edited by Max-Planck-Institut für Mathematik. Providence, Rhode Island: American Mathematical Society, 2016.

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21

Fonseca, Carlos M. da. A panorama of mathematics: Pure and applied : Conference on Mathematics and Its Applications, November 14-17, 2014, Kuwait University, Safat, Kuwait. Providence, Rhode Island: American Mathematical Society, 2016.

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22

Vidyasagar, M. Control System Synthesis: A Factorization Approach. MIT Press, 1988.

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23

Vidyasagar, Mathukumalli. Control System Synthesis: A Factorization Approach, Part I. Morgan & Claypool Publishers, 2011.

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24

Kaashoek, Marinus A., André C. M. Ran, and Harm Bart. State Space Approach to Canonical Factorization with Applications. Birkhauser Verlag, 2010.

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25

State Space Approach to Canonical Factorization with Applications. Birkhäuser Boston, 2011.

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26

A State Space Approach To Canonical Factorization With Applications. Birkhauser Boston, 2010.

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27

Gohberg, Israel. Factorization and Integrable Systems. Springer, 2012.

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28

Wang, Guanghui, and Jonathan Wu. Guide to Three Dimensional Structure and Motion Factorization. Springer London, Limited, 2012.

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29

Symeonidis, Panagiotis, and Andreas Zioupos. Matrix and Tensor Factorization Techniques for Recommender Systems. Springer London, Limited, 2016.

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30

Vidyasagar, Mathukumalli. Control Systems Synthesis: A Factorization Approach, Part I. Springer International Publishing AG, 2011.

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31

Symeonidis, Panagiotis, and Andreas Zioupos. Matrix and Tensor Factorization Techniques for Recommender Systems. Springer, 2017.

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32

Vidyasagar, Mathukumalli. Control Systems Synthesis: A Factorization Approach, Part II. Springer International Publishing AG, 2011.

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33

Butz, Martin V., and Esther F. Kutter. Top-Down Predictions Determine Perceptions. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780198739692.003.0009.

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While bottom-up visual processing is important, the brain integrates this information with top-down, generative expectations from very early on in the visual processing hierarchy. Indeed, our brain should not be viewed as a classification system, but rather as a generative system, which perceives something by integrating sensory evidence with the available, learned, predictive knowledge about that thing. The involved generative models continuously produce expectations over time, across space, and from abstracted encodings to more concrete encodings. Bayesian information processing is the key to understand how information integration must work computationally – at least in approximation – also in the brain. Bayesian networks in the form of graphical models allow the modularization of information and the factorization of interactions, which can strongly improve the efficiency of generative models. The resulting generative models essentially produce state estimations in the form of probability densities, which are very well-suited to integrate multiple sources of information, including top-down and bottom-up ones. A hierarchical neural visual processing architecture illustrates this point even further. Finally, some well-known visual illusions are shown and the perceptions are explained by means of generative, information integrating, perceptual processes, which in all cases combine top-down prior knowledge and expectations about objects and environments with the available, bottom-up visual information.
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34

Horing, Norman J. Morgenstern. Equations of Motion with Particle–Particle Interactions and Approximations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0008.

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Starting with the equation of motion for the field operator ψ(x,t) of an interacting many-particle system, the n-particle Green’s function (Gn) equation of motion is developed, with interparticle interactions generating an infinite chain of equations coupling it to (n+1)- and (n−1)-particle Green’s functions (Gn+1 and Gn−1, respectively). Particularly important are the one-particle Green’s function equation with its coupling to the two-particle Green’s function and the two-particle Green’s function equation with its coupling to the three-particle Green’s function. To develop solutions, it is necessary to introduce non-correlation decoupling procedures involving the Hartree and Hartree-Fock approximations for G2 in the G1 equation; and a similar factorization “ansatz” for G3 in the G2 equation, resulting in the Sum of Ladder Diagrams integral equation for G2, with multiple Born iterates and finite collisional lifetimes. Similar treatment of the G11-equation for the joint propagation of one-electron and one-hole subject to mutual Coulomb attraction leads to bound electron-hole exciton states having a discrete hydrogen like spectrum of energy eigenstates. Its role in single-particle propagation is also discussed in terms of one-electron self-energy Σ‎ and the T-matrix
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35

Factorization and Integrable Systems: Summer School in Faro, Portugal, September 2000 (Operator Theory: Advances and Applications). Birkhäuser Basel, 2003.

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36

(Editor), Israel Gohberg, Nenad Manojlovic (Editor), and Antonio Ferreira Dos Santos (Editor), eds. Factorization and Integrable Systems: Summer School in Faro, Portugal, September 2000 (Operator Theory, Advances and Applications, V. 141). Birkhauser, 2003.

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37

Jr, Joseph J. Bongiorno, and Kiheon Park. Design of Linear Multivariable Feedback Control Systems: The Wiener–Hopf Approach using Transforms and Spectral Factorization. Springer, 2020.

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38

Jr, Joseph J. Bongiorno, and Kiheon Park. Design of Linear Multivariable Feedback Control Systems: The Wiener-Hopf Approach Using Transforms and Spectral Factorization. Springer International Publishing AG, 2021.

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39

High-performance equation solvers and their impact on finite element analysis. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1990.

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40

Multi-color incomplete Cholesky conjugate gradient methods for vector computers. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1986.

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