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Journal articles on the topic 'Simplex (Mathematics)'

Author: Grafiati

Published: 4 June 2021

Last updated: 17 February 2022

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1

Zeng, M., and W. Q. Tao. "A comparison study of the convergence characteristics and robustness for four variants of SIMPLE‐family at fine grids." Engineering Computations 20, no. 3 (May 1, 2003): 320–40. http://dx.doi.org/10.1108/02644400310467234.

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A comparative study is performed to reveal the convergence characteristics and the robustness of four variants in the semi‐implicit method for pressure‐linked equations (SIMPLE)‐family: SIMPLE, SIMPLE revised (SIMPLER), SIMPLE consistent (SIMPLEC), and SIMPLE extrapolation (SIMPLEX). The focus is concentrated in the solution at fine grid system. Four typical fluid flow and heat transfer problems are taken as the numerical examples (lid‐driven cavity flow, flow in an axisymmetric sudden expansion, flow in an annulus with inner surface rotating and the natural convection in a square enclosure). It is found that an appropriate convergence condition should include both mass conservation and momentum conservation requirements. For the four problems computed, the SIMPLEX always requires the largest computational time, the SIMPLER comes the next, and the computational time of SIMPLE and SIMPLEC are the least. As far as the robustness is concerned, the SIMPLE algorithm is the worst, the SIMPLER comes the next and the robustness of SIMPLEX and SIMPLEC are superior to the others. The SIMPLEC algorithm is then recommended, especially for the computation at a fine grid system. Brief discussion is provided to further reveal the reasons which may account for the difference of the four algorithms.

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2

Yeh, Wei-Chang, and H. W. Corley. "A simple direct cosine simplex algorithm." Applied Mathematics and Computation 214, no. 1 (August 2009): 178–86. http://dx.doi.org/10.1016/j.amc.2009.03.080.

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3

Kalai, Gil. "Linear programming, the simplex algorithm and simple polytopes." Mathematical Programming 79, no. 1-3 (October 1997): 217–33. http://dx.doi.org/10.1007/bf02614318.

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4

Neamtu, Marian. "Homogeneous simplex splines." Journal of Computational and Applied Mathematics 73, no. 1-2 (October 1996): 173–89. http://dx.doi.org/10.1016/0377-0427(96)00042-8.

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5

LE, HUILING, and DENNIS BARDEN. "ON SIMPLEX SHAPE SPACES." Journal of the London Mathematical Society 64, no. 2 (October 2001): 501–12. http://dx.doi.org/10.1112/s0024610701002332.

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The right-invariant Riemannian metric on simplex shape spaces in fact makes them particular Riemannian symmetric spaces of non-compact type. In the paper, the general properties of such symmetric spaces are made explicit for simplex shape spaces. In particular, a global matrix coordinate representation is suggested, with respect to which several geometric features, important for shape analysis, have simple and easily computable expressions. As a typical application, it is shown how to locate the Fréchet means of a class of probability measures on the simplex shape spaces, a result analogous to that for Kendall's shape spaces.

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6

Izumi, Shuzo. "Sufficiency of simplex inequalities." Proceedings of the American Mathematical Society 144, no. 3 (July 8, 2015): 1299–307. http://dx.doi.org/10.1090/proc12756.

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7

Nishiyama, Kenta. "Incomplete hypergeometric systems associated to $1$-simplex $\times $ $(n-1)$-simplex." Rocky Mountain Journal of Mathematics 49, no. 3 (June 2019): 913–28. http://dx.doi.org/10.1216/rmj-2019-49-3-913.

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8

MUBAYI, DHRUV, and RESHMA RAMADURAI. "Simplex Stability." Combinatorics, Probability and Computing 18, no. 3 (May 2009): 441–54. http://dx.doi.org/10.1017/s0963548309009705.

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A d-simplex is a collection of d + 1 sets such that every d of them has non-empty intersection and the intersection of all of them is empty. Fix k ≥ d + 2 ≥ 3 and let be a family of k-element subsets of an n-element set that contains no d-simplex. We prove that if $|\cG| \geq (1 - o(1))\binom{n-1 }{k-1}$, then there is a vertex x of such that the number of sets in omitting x is o(nk−1) (here o(1)→ 0 and n → ∞). A similar result when n/k is bounded from above was recently proved in [10].Our main result is actually stronger, and implies that if $|\cG| > (1 + \epsilon)\binom{n-1 }{ k-1}$ for any ϵ < 0 and n sufficiently large, then contains d + 2 sets A, A1, . . . ,Ad+1 such that the Ais form a d-simplex, and A contains an element of ∩j≠iAj for each i. This generalizes, in asymptotic form, a recent result of Vestraëte and the first author [18], who proved it for d = 1, ϵ = 0 and n ≥ 2k.

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9

Shiguo, Yang. "Geometric inequalities for a simplex." Mathematical Inequalities & Applications, no. 4 (2005): 727–33. http://dx.doi.org/10.7153/mia-08-67.

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10

Hu, Jian-Feng, and Ping-Qi Pan. "An efficient approach to updating simplex multipliers in the simplex algorithm." Mathematical Programming 114, no. 2 (February 15, 2007): 235–48. http://dx.doi.org/10.1007/s10107-007-0099-3.

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11

Klamkin, M. S. "Inequality for a Simplex." SIAM Review 27, no. 4 (December 1985): 576. http://dx.doi.org/10.1137/1027154.

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12

Congedo, Pietro Marco, Jeroen Witteveen, and Gianluca Iaccarino. "A simplex-based numerical framework for simple and efficient robust design optimization." Computational Optimization and Applications 56, no. 1 (May 23, 2013): 231–51. http://dx.doi.org/10.1007/s10589-013-9569-0.

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13

Devriendt, Karel, and Piet Van Mieghem. "The simplex geometry of graphs." Journal of Complex Networks 7, no. 4 (January 29, 2019): 469–90. http://dx.doi.org/10.1093/comnet/cny036.

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AbstractGraphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods, each of which highlights the properties of graphs in a unique way. Here, we discuss a novel approach to study graphs: the simplex geometry (a simplex is a generalized triangle). This perspective, proposed by Miroslav Fiedler, introduces techniques from (simplex) geometry into the field of graph theory and conversely, via an exact correspondence. We introduce this graph-simplex correspondence, identify a number of basic connections between graph characteristics and simplex properties, and suggest some applications as example.

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14

Rosenberg, Noah, and Richard Bagby. "Integral over a Simplex: 11039." American Mathematical Monthly 112, no. 6 (June 1, 2005): 572. http://dx.doi.org/10.2307/30037536.

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15

Stojkovic, Nebojsa, Predrag Stanimirovic, and Marko Petkovic. "Several modifications of simplex method." Filomat, no. 17 (2003): 169–76. http://dx.doi.org/10.2298/fil0317169s.

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We analyze the problem of finding the first basic solution in the two phases simplex algorithm. Also, a modification and several improvements of the simplex method are introduced. We report computational results on numerical examples from Netlib test set.

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16

Nabli, Hédi. "An overview on the simplex algorithm." Applied Mathematics and Computation 210, no. 2 (April 2009): 479–89. http://dx.doi.org/10.1016/j.amc.2009.01.013.

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17

Evans, D. J., and G. M. Megson. "A systolic simplex algorithm." International Journal of Computer Mathematics 38, no. 1-2 (January 1991): 1–30. http://dx.doi.org/10.1080/00207169108803954.

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18

Zhang, Wen-Jie, Shi-Yuan Wang, and Ya-Li Feng. "Novel Simplex Kalman Filters." Circuits, Systems, and Signal Processing 36, no. 2 (April 26, 2016): 879–93. http://dx.doi.org/10.1007/s00034-016-0323-6.

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19

Kabluchko, Z., and D. Zaporozhets. "Angles of the Gaussian Simplex." Journal of Mathematical Sciences 251, no. 4 (November 6, 2020): 480–88. http://dx.doi.org/10.1007/s10958-020-05107-2.

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20

Baker, G. B., and T. M. Mills. "Demonstrating the Nelder‐Mead simplex method." International Journal of Mathematical Education in Science and Technology 18, no. 3 (May 1987): 439–40. http://dx.doi.org/10.1080/0020739870180313.

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21

Garcia, Victor, and Jean Pedersen. "Mathematics, Models, and Magz, Part II: Investigating Patterns in Pascal's Simplex." Mathematics Magazine 87, no. 5 (December 2014): 362–76. http://dx.doi.org/10.4169/math.mag.87.5.362.

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22

Orlin, James B., Serge A. Plotkin, and Éva Tardos. "Polynomial dual network simplex algorithms." Mathematical Programming 60, no. 1-3 (June 1993): 255–76. http://dx.doi.org/10.1007/bf01580615.

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23

Lima, R., and J. Naudts. "Invariant faces of a simplex." Journal of Mathematical Analysis and Applications 112, no. 1 (November 1985): 279–89. http://dx.doi.org/10.1016/0022-247x(85)90292-6.

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24

Yang, Ruyue, Jingyi Xiong, and Feilong Cao. "Multivariate Stancu operators defined on a simplex." Applied Mathematics and Computation 138, no. 2-3 (June 2003): 189–98. http://dx.doi.org/10.1016/s0096-3003(02)00088-7.

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25

Xiaoyan, Li, Leng Gangsong, and Tang Lihua. "Inequalities for a simplex and any point." Mathematical Inequalities & Applications, no. 3 (2005): 547–57. http://dx.doi.org/10.7153/mia-08-50.

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26

Golomb, Michael, and Kit Hanes. "The Orthocenter of a Simplex: 11087." American Mathematical Monthly 112, no. 10 (December 1, 2005): 936. http://dx.doi.org/10.2307/30037650.

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27

Jiang, Tao, Oleg Pikhurko, and Zelealem Yilma. "Set Systems without a Strong Simplex." SIAM Journal on Discrete Mathematics 24, no. 3 (January 2010): 1038–45. http://dx.doi.org/10.1137/090760775.

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28

Edmonds, Allan L. "The Geometry of an Equifacetal Simplex." Mathematika 52, no. 1-2 (December 2005): 31–45. http://dx.doi.org/10.1112/s0025579300000310.

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29

Pedersen, Pauli. "Modified simplex optimization program." Communications in Numerical Methods in Engineering 10, no. 4 (April 1994): 303–12. http://dx.doi.org/10.1002/cnm.1640100405.

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30

Shim, Sangho, Ellis L. Johnson, and Wenwei Cao. "Primal-dual simplex method for shooting." Electronic Notes in Discrete Mathematics 36 (August 2010): 719–26. http://dx.doi.org/10.1016/j.endm.2010.05.091.

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31

Mo, Jiangtao, Liqun Qi, and Zengxin Wei. "A network simplex algorithm for simple manufacturing network model." Journal of Industrial & Management Optimization 1, no. 2 (2005): 251–73. http://dx.doi.org/10.3934/jimo.2005.1.251.

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32

Cameron, Neil. "Stationarity in the simplex method." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 43, no. 1 (August 1987): 137–42. http://dx.doi.org/10.1017/s1446788700039513.

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AbstractDegeneracies occur with increasing frequency in some large scale linear programming problems, but with a simple change to the (revised) simplex method, resulting stationarity of the algorithm can be reduced. The method introduced here may also prevent cycling; neither the lexicographic refinement of Dantzig, Orden and Wolfe nor the perturbation technique of Charnes may be required to prevent cycling.

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33

Et. al., Chandrasekhar Putcha,. "A Comprehensive Method for Arriving at Initial Feasible Solution for Optimization Problems in Engineering with Illustrative Examples." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 5 (April 11, 2021): 1189–205. http://dx.doi.org/10.17762/turcomat.v12i5.1785.

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Two methods have been used extensively for arriving at initial basic feasible solution (IBF). One of them is Northwest corner rule and the other on is Russell method (Hillier & Lieberman, 2005.) Both methods have drawbacks. The IBF obtained is either far from optimal solution or does not have adequate number of entries to initiate transportation simplex algorithm. The Northwest Corner rule gives an initial feasible solution that is far from optimal while the IBF solution obtained using Russell method doesn’t give enough number of entries to start the transportation simplex algorithm. Hence, there is a need for developing a method for arriving at initial basic feasible solution with adequate number of entries needed to initiate transportation simplex algorithm, which can then be used to get an optimal solution. A computer software has been developed based on the new proposed method for this purpose. The proposed new method has been validated through four simple but illustrative examples.

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34

Coope, Ian, and Rachael Tappenden. "Efficient calculation of regular simplex gradients." Computational Optimization and Applications 72, no. 3 (January 30, 2019): 561–88. http://dx.doi.org/10.1007/s10589-019-00063-3.

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35

Neamtu, Marian. "On discrete simplex splines and subdivision." Journal of Approximation Theory 70, no. 3 (September 1992): 358–74. http://dx.doi.org/10.1016/0021-9045(92)90066-w.

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36

Berens, H., H. J. Schmid, and Y. Xu. "Bernstein-Durrmeyer polynomials on a simplex." Journal of Approximation Theory 68, no. 3 (March 1992): 247–61. http://dx.doi.org/10.1016/0021-9045(92)90104-v.

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37

El-Gebeily *, M. A., and Y. A. Fiagbedzi. "On certain properties of the regularn-simplex." International Journal of Mathematical Education in Science and Technology 35, no. 4 (July 2004): 617–29. http://dx.doi.org/10.1080/0020739042000232565.

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38

Cohen, Elaine, T. Lyche, and R. F. Riesenfeld. "Cones and recurrence relations for simplex splines." Constructive Approximation 3, no. 1 (December 1987): 131–41. http://dx.doi.org/10.1007/bf01890559.

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39

Bulut, Hasan. "Multiloop transportation simplex algorithm." Optimization Methods and Software 32, no. 6 (December 9, 2016): 1206–17. http://dx.doi.org/10.1080/10556788.2016.1260568.

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40

Si, Lin, Ge1 Xiong, and Gang-song Leng. "The john theorem for simplex." Journal of Shanghai University (English Edition) 10, no. 6 (December 2006): 487–90. http://dx.doi.org/10.1007/s11741-006-0043-4.

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41

Sbibih, D. "Bivariate Simplex Spline Quasi-Interpolants." Numerical Mathematics: Theory, Methods and Applications 3, no. 1 (June 2010): 97–118. http://dx.doi.org/10.4208/nmtma.2009.m9004.

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42

Păltănea, Radu. "A Second Order Weighted Modulus on a Simplex." Results in Mathematics 53, no. 3-4 (June 29, 2009): 361–69. http://dx.doi.org/10.1007/s00025-008-0347-8.

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43

Ivansic, Ivan. "A selection theorem for simplex-valued maps." Glasnik Matematicki 39, no. 2 (December 15, 2004): 331–33. http://dx.doi.org/10.3336/gm.39.2.14.

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44

Forcade, Rod, and Jack Lamoreaux. "Lattice-Simplex Coverings and the 84-Shape." SIAM Journal on Discrete Mathematics 13, no. 2 (January 2000): 194–201. http://dx.doi.org/10.1137/s0895480198349622.

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45

Dekster, B. V., and J. B. Wilker. "Edge lengths guaranteed to form a simplex." Archiv der Mathematik 49, no. 4 (October 1987): 351–66. http://dx.doi.org/10.1007/bf01210722.

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46

Faybusovich, Leonid. "Simplex method and groups generated by reflections." Acta Applicandae Mathematicae 20, no. 3 (September 1990): 231–45. http://dx.doi.org/10.1007/bf00049569.

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47

Gärtner, Bernd, Martin Henk, and Günter M. Ziegler. "Randomized Simplex Algorithms on Klee-Minty Cubes." COMBINATORICA 18, no. 3 (March 1998): 349–72. http://dx.doi.org/10.1007/pl00009827.

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48

Bossert, Walter, and Hans Peters. "Choice on the simplex domain." Journal of Mathematical Economics 84 (October 2019): 63–72. http://dx.doi.org/10.1016/j.jmateco.2019.07.002.

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49

Fiagbedzi *, Y. A., and M. El-Gebeily. "Classroom note: The inscribed sphere of ann-simplex." International Journal of Mathematical Education in Science and Technology 35, no. 2 (March 2004): 261–68. http://dx.doi.org/10.1080/00207390310001638269.

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50

Klamkin, M. S. "Inequality for a Simplex (M. S. Klamkin)." SIAM Review 28, no. 4 (December 1986): 579–80. http://dx.doi.org/10.1137/1028174.

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