Relevant bibliographies by topics / Matrice de Seidel

Academic literature on the topic 'Matrice de Seidel'

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Published: 18 May 2024

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Journal articles on the topic "Matrice de Seidel"

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Manjhi, Pankaj Kumar, and Ninian Nauneet Kujur. "On Goethals and Seidel Array." Indian Journal Of Science And Technology 17, no. 16 (April 19, 2024): 1643–46. http://dx.doi.org/10.17485/ijst/v17i16.2937.

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Objectives: In this article, we aim to find a series of Hadamard matrices by suitable selection of the special class of matrices given in the Goethals and Seidel array and study the pattern obtained. Methods: In the presented work, the search technique of Hadamard matrices has been done by selecting special class of (0,1) negacyclic matrices instead of the back diagonal identity matrix given in Geothals and Seidel arrays and the possible existence of negacyclic matrices for the corresponding four matrices have been explored in each case. Findings: Corresponding to the special class of (0,1) negacyclic matrices, no sets of four negacyclic matrices have been obtained in the Goethal Seidel array, for even orders. For odd orders, except in the case when all four matrices are equal and the case when there is a pair of equal matrices, many outputs have been obtained for the remaining cases, the search domain being upto 11,9 and 7 for the case of two different, three different and four different matrices respectively, in the Goethal Seidel array. Novelty: The selection of special class of negacyclic matrices instead of the back diagonal identity matrix and finding the corresponding four negacyclic matrices in Goethals and Seidel arrays for constructing Hadamard matrices provides a new approach to the construction of Hadamard matrices. Keywords: Hadamard matrix, Circulant matrix, Williamson matrices, Orthogonal array, Goethals and Seidel array
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Askari, Jalal. "A note on the Seidel and Seidel Laplacian matrices." Boletim da Sociedade Paranaense de Matemática 41 (December 23, 2022): 1–6. http://dx.doi.org/10.5269/bspm.51593.

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In this paper we investigate the spectrum of the Seidel and Seidel Laplacian matrix of a graph. We generalized the concept of Seidel Laplacian matrix which denoted by Seidel matrix and obtained some results related to them. This can be intuitively understood as a consequence of the relationship between the Seidel and Seidel Laplacian matrix in the graph by Zagreb index. In closing, we mention some alternatives to and generalization of the Seidel and Seidel Laplacian matrices. Also, we obtain relation between Seidel and Seidel Laplacian energy, related to all graphs with order n.
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Enyew, Tesfaye Kebede, Gurju Awgichew, Eshetu Haile, and Gashaye Dessalew Abie. "Second-refinement of Gauss-Seidel iterative method for solving linear system of equations." Ethiopian Journal of Science and Technology 13, no. 1 (April 30, 2020): 1–15. http://dx.doi.org/10.4314/ejst.v13i1.1.

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Although large and sparse linear systems can be solved using iterative methods, its number of iterations is relatively large. In this case, we need to modify the existing methods in order to get approximate solutions in a small number of iterations. In this paper, the modified method called second-refinement of Gauss-Seidel method for solving linear system of equations is proposed. The main aim of this study was to minimize the number of iterations, spectral radius and to increase rate of convergence. The method can also be used to solve differential equations where the problem is transformed to system of linear equations with coefficient matrices that are strictly diagonally dominant matrices, symmetric positive definite matrices or M-matrices by using finite difference method. As we have seen in theorem 1and we assured that, if A is strictly diagonally dominant matrix, then the modified method converges to the exact solution. Similarly, in theorem 2 and 3 we proved that, if the coefficient matrices are symmetric positive definite or M-matrices, then the modified method converges. And moreover in theorem 4 we observed that, the convergence of second-refinement of Gauss-Seidel method is faster than Gauss-Seidel and refinement of Gauss-Seidel methods. As indicated in the examples, we demonstrated the efficiency of second-refinement of Gauss-Seidel method better than Gauss-Seidel and refinement of Gauss-Seidel methods.
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Zhang, Cheng-yi, Dan Ye, Cong-Lei Zhong, and SHUANGHUA SHUANGHUA. "Convergence on Gauss-Seidel iterative methods for linear systems with general H-matrices." Electronic Journal of Linear Algebra 30 (February 8, 2015): 843–70. http://dx.doi.org/10.13001/1081-3810.1972.

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It is well known that as a famous type of iterative methods in numerical linear algebra, Gauss-Seidel iterative methods are convergent for linear systems with strictly or irreducibly diagonally dominant matrices, invertible H−matrices (generalized strictly diagonally dominant matrices) and Hermitian positive definite matrices. But, the same is not necessarily true for linear systems with non-strictly diagonally dominant matrices and general H−matrices. This paper firstly proposes some necessary and sufficient conditions for convergence on Gauss-Seidel iterative methods to establish several new theoretical results on linear systems with nonstrictly diagonally dominant matrices and general H−matrices. Then, the convergence results on preconditioned Gauss-Seidel (PGS) iterative methods for general H−matrices are presented. Finally, some numerical examples are given to demonstrate the results obtained in this paper.
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Dil, Ayhan, and Mirac Cetin Firengiz. "Shifted Euler-Seidel matrices." Miskolc Mathematical Notes 18, no. 1 (2017): 173. http://dx.doi.org/10.18514/mmn.2017.1662.

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Szöllősi, Ferenc, and Patric R. J. Östergård. "Enumeration of Seidel matrices." European Journal of Combinatorics 69 (March 2018): 169–84. http://dx.doi.org/10.1016/j.ejc.2017.10.009.

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TUTAŞ, Nesrin. "Euler-Seidel matrices over F_p." TURKISH JOURNAL OF MATHEMATICS 38 (2014): 16–24. http://dx.doi.org/10.3906/mat-1209-36.

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Vinsensia, Desi, Yulia Utami, Fathia Siregar, and Muhammad Arifin. "Improve refinement approach iterative method for solution linear equition of sparse matrices." Jurnal Teknik Informatika C.I.T Medicom 15, no. 6 (January 30, 2024): 306–13. http://dx.doi.org/10.35335/cit.vol15.2024.721.pp306-313.

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In this paper, systems of linear equations on sparse matrices investigated through modified improve method using Gauss-Seidel and successive overrelaxation (SOR) approach. Taking into adapted convergence rate on the Improve refinement Gauss-seidel outperformed the prior two Gauss-Seidel methods in terms of rate of convergence and number of iterations required to solve the problem by applying a modified version of the Gauss-Seidel approach. to observe the effectiveness of this method, the numerical example is given. The main findings in this study, that Gauss seidel improvement refinement gives optimum spectral radius and convergence rate. Similarly, the SOR improved refinement method gives. Considering their performance, using parameters such as time to converge, number of iterations required to converge and spectral radius level of accuracy. However, SOR works with relaxation values so that it greatly affects the convergence rate and spectral radius results if given greater than 1.
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Shen, Shuhui, and Xiaojun Zhang. "Constructions of Goethals–Seidel Sequences by Using k-Partition." Mathematics 11, no. 2 (January 6, 2023): 294. http://dx.doi.org/10.3390/math11020294.

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In this paper, we are devoted to finding Goethals–Seidel sequences by using k-partition, and based on the finite Parseval relation, the construction of Goethals–Seidel sequences could be transformed to the construction of the associated polynomials. Three different structures of Goethals–Seidel sequences will be presented. We first propose a method based on T-matrices directly to obtain a quad of Goethals–Seidel sequences. Next, by introducing the k-partition, we utilize two classes of 8-partitions to obtain a new class of polynomials still remaining the same (anti)symmetrical properties, with which a quad of Goethals–Seidel sequences could be constructed. Moreover, an adoption of the 4-partition together with a quad of four symmetrical sequences can also lead to a quad of Goethals–Seidel sequences.
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Dessalew, Gashaye, Tesfaye Kebede, Gurju Awgichew, and Assaye Walelign. "Generalized Refinement of Gauss-Seidel Method for Consistently Ordered 2-Cyclic Matrices." Abstract and Applied Analysis 2021 (May 31, 2021): 1–7. http://dx.doi.org/10.1155/2021/8343207.

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This paper presents generalized refinement of Gauss-Seidel method of solving system of linear equations by considering consistently ordered 2-cyclic matrices. Consistently ordered 2-cyclic matrices are obtained while finite difference method is applied to solve differential equation. Suitable theorems are introduced to verify the convergence of this proposed method. To observe the effectiveness of this method, few numerical examples are given. The study points out that, using the generalized refinement of Gauss-Seidel method, we obtain a solution of a problem with a minimum number of iteration and obtain a greater rate of convergence than other previous methods.
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Dissertations / Theses on the topic "Matrice de Seidel"

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Lehbab, Imène. "Problèmes métriques dans les espaces de Grassmann." Electronic Thesis or Diss., Mulhouse, 2023. http://www.theses.fr/2023MULH6508.

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Il s'agit d'une contribution dans le domaine de la géométrie métrique du plan projectif complexe CP2 et de la variété de Grassmann réelle des plans dans R6. On s'intéresse à l'étude de tous les p-uplets, p ≥ 3, de droites équiangulaires dans C3 et des p-uplets de plans équi-isoclins dans R6. Sachant que 9 est le nombre maximum de droites équiangulaires que l'on peut construire dans C3, on décrit une méthode qui permet de construire tous les p-uplets de droites équiangulaires pour tout pϵ[3,9]. En particulier, on construit dans C3 cinq classes de congruence de quadruplets de droites équiangulaires dont une dépend d'un paramètre réel ɣ que l'on étend à une famille infinie de sextuplets de droites équiangulaires dépendant du même paramètre réel ɣ. En outre, on donne les angles pour lesquels nos sextuplets s'étendent au-delà et jusqu'aux 9-uplets. On sait qu'il existe un p-uplet, p≥3, de plans équi-isoclins engendrant Rr, r≥4, de paramètre c, 0
This work contributes to the field of metric geometry of the complex projective plane CP2 and the real Grassmannian manifold of the planes in R6. More specifically, we study all p-tuples, p ≥ 3, of equiangular lines in C3 or equidistant points in CP2, and p-tuples of equi-isoclinic planes in R6. Knowing that 9 is the maximum number of equiangular lines that can be constructed in C3, we develop a method to obtain all p-tuples of equiangular lines for all p ϵ [3,9]. In particular, we construct in C3 five congruence classes of quadruples of equiangular lines, one of which depends on a real parameter ɣ, which we extend to an infinite family of sextuples of equiangular lines depending on the same real parameter ɣ. In addition, we give the angles for which our sextuples extend beyond and up to 9-tuples. We know that there exists a p-tuple, p ≥ 3, of equi-isoclinic planes generating Rr, r ≥ 4, with parameter c, 0< c <1, if and only if there exists a square symmetric matrix, called Seidel matrix, of p × p square blocks of order 2, whose diagonal blocks are all zero and the others are orthogonal matrices in O(2) and whose smallest eigenvalue is equal to - 1/c and has multiplicity 2p-r. In this thesis, we investigate the case r=6 and we also show that we can explicitly determine the spectrum of all Seidel matrices of order 2p, p ≥ 3 whose off-diagonal blocks are in {R0, S0} where R0 and S0 are respectively the zero-angle rotation and the zero-angle symmetry. We thus show an unexpected link between some p-tuples of equi-isoclinic planes in Rr and simple graphs of order p
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Lesueur, Teddy. "Développement d’un nouveau bio-essai survie croissance copépodes "BASIC" : application et validation sur différentes matrices environnementales." Thesis, Le Havre, 2014. http://www.theses.fr/2014LEHA0019/document.

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L’estuaire de Seine est l’un des plus pollués de l’hémisphère nord dû notamment à ses activités urbaines et agricoles de son bassin versant. Malgré cela le copépode E. affinis représente 90 % de la biomasse zooplanctonique en estuaire de Seine. L’objectif de la thèse était de développer un nouveau Bio-essAi Survie Croissance copépode (BASIC) à l’aide du copépode E. affinis sur différentes matrices environnementales. Dans un premier temps, le bio-essai a été mise au point à l’aide de sédiments enrobés avec des molécules modèles représentatives de la contamination estuarienne (APs, HAPS et PCBs) avant d’être validé, par la suite, sur des sédiments naturels de l’estuaire de Seine. Le bio-essai à ensuite été appliqué en solution au 4-NP et au PCB 126 et sur Vibrio anguillarum issus de l’estuaire de Seine. Un protocole d’exposition multi-générationnel a été appliqué dans les mêmes conditions pendant trois générations. Les résultats recensés ont montré un effet sur le développement larvaire lors des expositions après 6 jours d’expositions à des sédiments enrobés. Dans le cadre des expositions en solution, des résultats similaires ont été obtenus, notamment, un retard de croissance après deux jours d’exposition au 4-NP et au PCB 126 corrélé avec les niveaux d’activité chitobiase. En revanche, à la fin de l’expérimentation ce résultat n’est plus observé. Lors des expositions à Vibrio anguillarum, une augmentation de l’activité chitobiase a été enregistrée les premiers jours de l’exposition, impliquant une augmentation de la croissance au sixième jour. Dans le cadre des expérimentions multi-générationnelle, le copépode semble se stabiliser à la troisième génération
Seine estuary is one of the most polluted in the northern hemisphere largely due to its urban and agricultural activities of its watershed. Despite this the copepod E. affinis represents 90% of zooplankton biomass in the Seine estuary. The aim of the thesis was to develop a new bioassay Survival Growth copepod with the copepod E. affinis on various environmental matrices. Initially, the bioassay was developed using sediments spiked with molecules representative models of estuarine contamination (APs, PAHS and PCBs) before being validated on natural sediments of the Seine estuary. The bioassay was applied in solution 4-NP and PCB 126 and Vibrio anguillarum from the Seine estuary. A multi-generational exposure protocol was applied under the same conditions for three generations. The results showed an effect on larval development after 6 days of exposure to sediments. In solution, similar results were obtained, including, retarded growth after two days of exposure to 4-NP and PCB 126 correlated with chitobiase activity levels. However, at the end of the experiment the result is not observed. At exposition with Vibrio anguillarum, increased activity was recorded chitobiase the first days, involving an increase in growth in the sixth day. As part of the multi-generational experimenting, the copepod appears to be stabilizing at the third generation
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Wen, Huang Ching, and 黃靜文. "Gauss-Seidel Method and its Improving Versions for Solving H-matrices Linear Systems." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/48974875007070889998.

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碩士
輔仁大學
數學系研究所
96
Solving linear system with H-matrix appeared in many applications and is studied by many numerical calculation researchers. In this thesis we first introduced some algorithms to judge the H-matrix. Then we applied the Gauss-Seidel method and its improving versions, MGS and IMGS, to solve such linear systems and systems with their corresponding comparison matrices. Both theoretical and numerical experiments have shown that the modified methods yield considerable improvement in the convergence rate, especially the IMGS method with suitable parameter α.
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Books on the topic "Matrice de Seidel"

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1942-, Corneil D. G., and Mathon R. A, eds. Geometry and combinatorics: Selected works of J.J. Seidel. Boston: Academic Press, 1991.

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Jaekel, Charlotte, ed. Thomas Meinecke. edition text + kritik im Richard Boorberg Verlag, 2021. http://dx.doi.org/10.5771/9783967075410.

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Romancier, Musiker, DJ, Journalist, Radio-Moderator und Produzent von Hörspielen: Thomas Meinecke – zuletzt ausgezeichnet mit dem Berliner Literaturpreis (2020) – ist so vielseitig wie kaum ein Schriftsteller der Gegenwart. Romane wie "The Church of John F. Kennedy", "Tomboy", "Lookalikes" oder "Selbst" spannen ein dynamisches, diskursives Netz, das neue Welten aus disparaten Fragmenten aufscheinen lässt. Sie provozieren, weil sie konventionelle Gattungsmuster und Kulturtechniken, gesellschaftliche Normen und geläufige Dichotomien unterlaufen. Ihre 'ozeanische' Ästhetik erweitert das popkulturelle Universum, verbindet Sounds der Popmusik mit Theologie, Ethnografie, Psychoanalyse und Queerness, verwebt schöne Literatur mit 'schöner Theorie'. Meineckes so virtuose wie spielerische Bewegung zwischen High und Low macht ihn zum zentralen Autor der Gegenwartsliteratur, der einen produktiven Diskurs um die Frage von Autorschaft anregt, was sich nicht zuletzt in seinen Poetik-Dozenturen bisher u. a. in Frankfurt, Köln und Berlin niederschlägt. Die Beiträge des Heftes loten die poetologisch-theoretische Matrix und materielle Basis von Meineckes vielschichtigem Werk aus. Sie fragen nach dem Verhältnis von Intertextualität und Plagiat, widmen sich seiner Bibliomanie, Musikaffinität und Gegenwartsemphase, fokussieren die popkulturelle Oberflächenästhetik, erzählerische Ethik und mittelalterliche Mystik.
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Book chapters on the topic "Matrice de Seidel"

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Pötzsch, Holger. "Spielend bilden?" In Game Studies, 307–22. Bielefeld, Germany: transcript Verlag, 2024. http://dx.doi.org/10.14361/9783839467978-018.

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In seinem Beitrag operationalisiert Holger Pötzsch das Cybermedia-Modell von Espen Aarseth und Gordon Calleja und stellt eine Matrize für eine systematische Evaluierung von Videospielen vor deren Gebrauch im Unterricht vor. Ausgehend von den Feldern Zeichen und Repräsentation, Spielregeln und -mechaniken, Materialität und politische Ökonomie sowie institutionelle Rahmen, ermöglicht die Matrize das Stellen einer Reihe spezifischer Fragen, die vor didaktischer Nutzung reflektiert und geklärt werden müssen. Der Beitrag hofft so, einer kritischen Nutzung des Mediums Videospiel in schulischen Kontexten Vorschub leisten zu können.
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Arnold, Stefan, and Martina Wagner-Egelhaaf. "Begründung und Geltung. Rhetorische Verflechtungen von Recht und Literatur." In Rhetoriken zwischen Recht und Literatur, 177–94. Berlin, Heidelberg: Springer Berlin Heidelberg, 2023. http://dx.doi.org/10.1007/978-3-662-66928-0_10.

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ZusammenfassungRecht und Literatur bzw. Rechts- und Literaturwissenschaft sind über die Rhetorik historisch und systematisch miteinander verbunden. Allerdings hat die Rhetorik in beiden Disziplinen einen unterschiedlichen Stellenwert: Während die Rhetorik in der Literaturwissenschaft ein prominentes Instrumentarium der Textanalyse darstellt, dabei aber oft auf die Figurenlehre reduziert wird, ist ihr Ansehen in der Rechtswissenschaft eher gering, insofern Rhetorik als etwas der juristischen ,Wahrheit‘ Hinzugefügtes begriffen wird. Der Beitrag argumentiert dafür, dass jede Redeäußerung grundsätzlich eine rhetorische Dimension hat und verweist auf die produktive Vielgestaltigkeit der Rhetorik. Insbesondere nimmt er Geltungsbegründungen in Rechts- und Literaturwissenschaft in den Blick, indem er auf der einen Seite zeigt, wie in der Poetik des 18. Jahrhunderts Geltung rhetorisch erzeugt wird, und auf der anderen Seite die rhetorische Verfasstheit von Gerichtsurteilen als Untersuchungsbereich vorstellt. Außerdem wird eine Matrix zur differenzierten Erfassung des Geltungsbegriffs vorgestellt.
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Elman, Howard C. "Iterative Methods for Linear Systems." In Large-Scale Matrix Problems and the Numerical Solution of Partial Differential Equations, 69–118. Oxford University PressOxford, 1994. http://dx.doi.org/10.1093/oso/9780198534631.003.0003.

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Abstract In Section 2, we introduce the basic ideas of stationary iterative methods and consider several particular examples of these, namely the Jacobi, Gauss- Seidel, SOR, and SSOR methods. We outline some results on the convergence of them, for both general matrices and those with special structure. In Section 3, we give an overview of Krylov subspace methods for systems where the coefficient matrix is symmetric.
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Charhbili, Mohamed, Amina El Yaagoubi, Renaud Di Francesco, and Lamia Berrah. "Matrices of Sets as a Mathematical Tool Enabling Efficient Planning of Intermodal Freight Transport." In Advances in Logistics, Operations, and Management Science, 82–103. IGI Global, 2023. http://dx.doi.org/10.4018/978-1-6684-8474-6.ch004.

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This research is a component of the FLUSYNCHRO initiative and is focused on constructing a decision support tool for comparing multimodal transport routes from one point to another based on several factors, including distance, time, and environmental considerations. The study employs the innovative theoretical framework of matrices of sets to model container-based intermodal transportation with a particular emphasis on river, rail, and road modalities as well as environmental externalities. The intermodal transport network is presented as a multi-level graph, with each level represented by a matrix of sets comprising terminals, links, and data of the corresponding mode of transport. The determination of multimodal paths is achieved through the multiplication of associated matrices of sets of each mode. The Seine Axis is the region to which this investigation applies, as all three transport modes are accessible. The principal goal is to promote the usage of environmentally sustainable intermodal transportation systems.
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Albreem, Mahmoud. "Efficient Iterative Massive MIMO Detectors Based on Iterative Matrix Inversion Methods." In Design Methodologies and Tools for 5G Network Development and Application, 175–95. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-4610-9.ch009.

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Massive multiple-input multiple-output (MIMO) is a key technology in fifth generation (5G) communication systems. Although the maximum likelihood (ML) obtains an optimal performance, it is prohibited in realization because of its high computational complexity. Linear detectors are an alternative solution, but they contain a matrix inversion which is not hardware friendly. Several methods have been proposed to approximate or to avoid the computation of exact matrix inversion. This chapter garners those methods and study their applicability in massive MIMO system so that a generalist in communication systems can differentiate between different algorithms from a wide range of solutions. This chapter presents the performance-complexity profile of a detector based on the Neuamnn-series (NS), Newton iteration (NI), successive over relaxation (SOR), Gauss-Seidel (GS), Jacobi (JA), Richardson (RI), optimized coordinate descent (OCD), and conjugate-gradient (CG) methods in 8×64, 16×64, and 32×64 MIMO sizes, and modulation scheme is 64QAM.
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Francescon, Leonardo. "Toru Takemitsu, Between Tides: al di là del suono e del silenzio Analisi generale e riflessioni personali sull’opera." In L’estetica del vuoto Vuoti, pieni, suoni, silenzi, presenze, assenza. Venice: Fondazione Università Ca’ Foscari, 2023. http://dx.doi.org/10.30687/978-88-6969-701-2/007.

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This article is born from my personal reflections while studying Between Tides, therefore contributing to the already existing literature of Toru Takemitsu. A general analysis outlines the structural motives as Sea Theme, played with E Flat, E and A, constitutes a matrix of other thematic cells. The piano writing chosen aim to disassociate timbres underlining the colors of every harmony, while the strings produce a sonorous effect with techniques and positions that go back to the avante-garde of the 1900s. In Between Tides we hear an assiduous research of the sound and beyond it. Playing this work creates a unique performing experience where gesture and sound are inextricably bound together in an intimate relationship, where the sensitivity of Toru Takemitsu was able to seize.
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Parker, Robert. "Introduction." In Miasma, 1–17. Oxford University PressOxford, 1990. http://dx.doi.org/10.1093/oso/9780198147428.003.0001.

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Abstract Anyone who has sampled a few of the most commonly read Greek texts will have encountered pollution. In tragedy, the plague at the opening of the Oedipus Tyrannus is caused by it, it precipitates Creon’s repentance in the Antigone, while Orestes in the Oresteia, although he is driven to the matricide by the fear of one pollution, is seized by another after performing it. In history, it plays, perhaps, a larger part than any other religious motif in the austere Thucydides. A Greek state in the fifth century, we learn from him, might attribute a natural disaster to a pollution it had incurred, and he shows us the Athenians expelling the Delians from their island to ensure the purity of this religious centre. In the fourth century, Aeschines could envisage Demosthenes as the ‘demon who pollutes all Greece’, and brings it to misfortune. A glance at evidence of a different kind, inscriptions regulating cult, shows how the concern for purity affected the individual in his everyday religious practice. The threat of pollution is, it seems, the dominating concern of the Superstitious Man of Theophrastus.
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Conference papers on the topic "Matrice de Seidel"

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Liu, Qingbing. "Convergence of the Modified Gauss-Seidel Method for H-matrices." In Third International Conference on Natural Computation (ICNC 2007). IEEE, 2007. http://dx.doi.org/10.1109/icnc.2007.317.

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Koester, D. P., S. Ranka, and G. C. Fox. "A parallel Gauss-Seidel algorithm for sparse power system matrices." In the 1994 ACM/IEEE conference. New York, New York, USA: ACM Press, 1994. http://dx.doi.org/10.1145/602770.602806.

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Darvishi, M. T., M. Azimbeigi, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "A New Preconditioner on Gauss-Seidel Method for H-Matrices." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241458.

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Liao, Qing, Naiyang Guan, and Qian Zhangg. "Gauss-Seidel based non-negative matrix factorization for gene expression clustering." In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016. http://dx.doi.org/10.1109/icassp.2016.7472100.

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Naik, Teja U., and Nitesh Guinde. "Implementing the gauss seidel algorithm for solving eigenvalues of symmetric matrices with CUDA." In 2017 International Conference on Computing Methodologies and Communication (ICCMC). IEEE, 2017. http://dx.doi.org/10.1109/iccmc.2017.8282601.

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Zhao, Di, and Hongyi Li. "A modified Gauss-Seidel iterative algorithm for H-matrix with centrosymmetric structure." In 2011 IEEE 3rd International Conference on Communication Software and Networks (ICCSN). IEEE, 2011. http://dx.doi.org/10.1109/iccsn.2011.6013805.

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Zhang, Shi-Guang, and Ting Zhou. "Comparison theorems between the preconditioned Gauss-Seidel method and the AOR method for M-matrices." In 2017 7th International Conference on Advanced Design and Manufacturing Engineering (ICADME 2017). Paris, France: Atlantis Press, 2017. http://dx.doi.org/10.2991/icadme-17.2017.84.

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Pao, Y. C., and Erik L. Ritman. "Generalized Algorithms for Interactive Warping Analysis of Porous Cross Sections." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/cie-9070.

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Abstract Algorithms have been developed for warping analysis and calculation of the shearing stresses in a general porous cross section of a long rod when it is subjected to twisting torques at its ends. The shape and dimensions of the cross section full of holes are defined from the binary segmented image data with by a micro-CT scanning technique. Finite difference approximation of the Laplace equation governing the cross-sectional warping leading to the matrix solution by a Gauss-Seidel process is discussed. Method of pointer matrix which keeps the locations of the nonzero elements of the coefficient matrix, is employed to expedite the iterative solution. Computer programs are coded in QuickBASIC language to facilitate plotting of the computed distributions of warping and shearing stresses. The classical torsional problem of square and thin-walled cross sections are used to reexamine the accuracy of the developed algorithms and results are found to be in very good agreement.
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9

Lu, Yi, Xin Yuan, and W. N. Dawes. "Investigation of 3D Internal Flow Using New Flux-Reconstruction High Order Method." In ASME Turbo Expo 2012: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/gt2012-69270.

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The new godunov-type high order method via flux-reconstruction, are capable of unifiying several popular methods including the discontinuous Galerkin, staggered-grid multi-domain method, or the spectral difference/spectral volume methods into a single family. Compared to discontinuous galerkin method, this new method retain the arbitrary order and compact properties but written in differential form and without mass matrix. The flux-reconstrcution method using general unstructured 2D/3D mesh including triangles, quadrilaterals, tetrahedrons, pyramids, prisms and hexahedrons are implemented. Compared to discontinuous galerkin method, FR is differential form without any quandature, so it runs faster and is easier to implement on GPU to achieve higher speed up ratio. The present paper investigates three different solving methods for this new method in order to cut down the hugh computational cost and memory requirement for fully implicit methods. Explicit multi-stage Runge-Kutta, nonlinear Lower-Upper Symmetry Gauss-Seidel (LU-SGS) and generalized minimal residual (GMRES) with matrix-free preconditioning methods are implemented and all these three methods use p-multigrid to smooth low-frequency errors on lower order. The results of 2D steady-state external/internal viscous flows are presented and the convergence properties for different solving method are compared. Efficiency and robustness are improved through symmetric Gauss-Seidel (SGS) iterations as preconditioning, a remarkable feature of the present GMRES+SGS method is that the storage of the full Jacobian matrix can be eliminated and only its diagonal stored. A laplacian artificial viscosity is tested to capture shock in one element and performs well for this new high order method, an L2 projection method is used to improve the perfomance of aliasing error in conservative form. The one equation Spalart-Allmaras turbulence model is unsed to solve the Raynolds average navier-stokes equations. MPI is used for parallel simulations for ralatively complex 3D internal flow when using high order method. Compared to other high order methods, results in this paper show that Flux-Reconstruction methods with efficient solving method performs well for 2D/3D general unstructured mesh in wide range of reynorlds number, and is also potential for “real geometry” simulations.
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10

Zhang, Sen, Hongbing Pu, Boqian Wang, Shenren Xu, Yong Zhang, Xiuquan Huang, and Dingxi Wang. "Implementation of a Newton−Krylov Algorithm in the Open-source Solver of PHengLEI." In GPPS Hong Kong24. GPPS, 2023. http://dx.doi.org/10.33737/gpps23-tc-124.

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This paper presents the implementation of a Newton–Krylov (NK) algorithm in the open-source solver of Platform for Hybrid ENGineering simulation of flows (PHengLEI). The linearized equation system is solved using the Generalized Minimal Residual Method (GMRES). The elements of the exact Jacobian matrix are first computed using the automatic differentiation tool of Sacado and then manually assembled. In this work, two solution strategies are investigated for the solution of the RANS equations and the turbulence model equation: a decoupled approach and a coupled approach. The decoupled approach solves the RANS equations and the turbulence model equation sequentially while the coupled approach solves the RANS equations and the turbulence model equation simultaneously. The NACA0012 airfoil is used as the test vehicle to examine the two solution strategies. Results from the Lower-Upper Symmetric-Gauss-Seidel method are also presented as references.
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