Academic literature on the topic 'Piecewise affine functions'

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Journal articles on the topic "Piecewise affine functions"

1

Gorokhovik, V. V., O. I. Zorko, and G. Birkhoff. "Piecewise affine functions and polyhedral sets∗." Optimization 31, no. 3 (1994): 209–21. http://dx.doi.org/10.1080/02331939408844018.

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2

Eghbal, Najmeh, Naser Pariz, and Ali Karimpour. "Discontinuous piecewise quadratic Lyapunov functions for planar piecewise affine systems." Journal of Mathematical Analysis and Applications 399, no. 2 (2013): 586–93. http://dx.doi.org/10.1016/j.jmaa.2012.09.054.

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3

Veeser, Andreas. "Positivity Preserving Gradient Approximation with Linear Finite Elements." Computational Methods in Applied Mathematics 19, no. 2 (2019): 295–310. http://dx.doi.org/10.1515/cmam-2018-0017.

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AbstractPreserving positivity precludes that linear operators onto continuous piecewise affine functions provide near best approximations of gradients. Linear interpolation thus does not capture the approximation properties of positive continuous piecewise affine functions. To remedy, we assign nodal values in a nonlinear fashion such that their global best error is equivalent to a suitable sum of local best errors with positive affine functions. As one of the applications of this equivalence, we consider the linear finite element solution to the elliptic obstacle problem and derive that its e
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4

Cheraghi-Shami, Farideh, Ali-Akbar Gharaveisi, Malihe M. Farsangi, and Mohsen Mohammadian. "Discontinuous Lyapunov functions for a class of piecewise affine systems." Transactions of the Institute of Measurement and Control 41, no. 3 (2018): 729–36. http://dx.doi.org/10.1177/0142331218771138.

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In this paper, a Lyapunov-based method is provided to study the local asymptotic stability of planar piecewise affine systems with continuous vector fields. For such systems, the state space is supposed to be partitioned into several bounded convex polytopes. A piecewise affine function, not necessarily continuous on the boundaries of the polytopic partitions, is proposed as a candidate Lyapunov function. Then, sufficient conditions for the local asymptotic stability of the system, including a monotonicity condition at switching instants, are formulated as a linear programming problem. In addi
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5

Kripfganz, Anita, and R. Schulze. "Piecewise affine functions as a difference of two convex functions." Optimization 18, no. 1 (1987): 23–29. http://dx.doi.org/10.1080/02331938708843210.

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6

Kari, Jarkko. "Piecewise Affine Functions, Sturmian Sequences and Wang Tiles." Fundamenta Informaticae 145, no. 3 (2016): 257–77. http://dx.doi.org/10.3233/fi-2016-1360.

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7

Donovan, G. C., J. S. Geronimo, and D. P. Hardin. "Compactly Supported, Piecewise Affine Scaling Functions on Triangulations." Constructive Approximation 16, no. 2 (2000): 201–19. http://dx.doi.org/10.1007/s003659910009.

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8

Xu, Jun, Ton J. J. van den Boom, Bart De Schutter, and Shuning Wang. "Irredundant lattice representations of continuous piecewise affine functions." Automatica 70 (August 2016): 109–20. http://dx.doi.org/10.1016/j.automatica.2016.03.018.

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9

Nguyen, Ngoc Anh, and Sorin Olaru. "A family of piecewise affine control Lyapunov functions." Automatica 90 (April 2018): 212–19. http://dx.doi.org/10.1016/j.automatica.2017.12.052.

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10

Adeeb, S., and V. G. Troitsky. "Locally piecewise affine functions and their order structure." Positivity 21, no. 1 (2016): 213–21. http://dx.doi.org/10.1007/s11117-016-0411-7.

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