Academic literature on the topic 'Application of linear algebra'

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Journal articles on the topic "Application of linear algebra"

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Fabregat-Traver, Diego, and Paolo Bientinesi. "Application-tailored linear algebra algorithms." International Journal of High Performance Computing Applications 27, no. 4 (July 18, 2013): 426–39. http://dx.doi.org/10.1177/1094342013494428.

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Deng, Ji Xia. "Application of Linear Algebra in Real Life." Applied Mechanics and Materials 556-562 (May 2014): 3392–95. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.3392.

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Linear algebra is an important basic course in university mathematics, finite dimensional vector space and linear transformation theory mainly on matrix theory, and the combination of matrix. Concept in linear algebra is defined directly by the mathematical symbol, rarely by example to import. How to make students master the abstract and difficult course, first of all is to let the students find the course in our daily life, to stimulate interest in learning.
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Lord, Nick, Charles G. Cullen, David C. Lay, Erwin Kleinfeld, and Margaret Kleinfeld. "Linear Algebra with Applications." Mathematical Gazette 82, no. 493 (March 1998): 153. http://dx.doi.org/10.2307/3620192.

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鞠, 桂玲. "Teaching Reform of Linear Algebra Based on Application." Creative Education Studies 08, no. 05 (2020): 688–91. http://dx.doi.org/10.12677/ces.2020.85112.

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杨, 威. "Application Examples of Linear Algebra Based on MATLAB." Advances in Applied Mathematics 08, no. 03 (2019): 424–29. http://dx.doi.org/10.12677/aam.2019.83048.

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Gohberg, Israel, Peter Lancaster, and Leiba Rodman. "A New Book in Linear Algebra: Indefinite Linear Algebra and Applications." Integral Equations and Operator Theory 53, no. 1 (September 2005): 149–51. http://dx.doi.org/10.1007/s00020-005-1356-6.

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Hoa, Dinh Trung, Toan Minh Ho, and Hiroyuki Osaka. "The Linear Span of Projections in AH Algebras and for Inclusions ofC*-Algebras." Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/204319.

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In the first part of this paper, we show that an AH algebraA=lim→(Ai,ϕi)has the LP property if and only if every element of the centre ofAibelongs to the closure of the linear span of projections inA. As a consequence, a diagonal AH-algebra has the LP property if it has small eigenvalue variation in the sense of Bratteli and Elliott. The second contribution of this paper is that for an inclusion of unitalC*-algebrasP⊂Awith a finite Watatani index, if a faithful conditional expectationE:A→Phas the Rokhlin property in the sense of Kodaka et al., thenPhas the LP property under the condition thatAhas the LP property. As an application, letAbe a simple unitalC*-algebra with the LP property,αan action of a finite groupGontoAut(A). Ifαhas the Rokhlin property in the sense of Izumi, then the fixed point algebraAGand the crossed product algebraA ⋊α Ghave the LP property. We also point out that there is a symmetry on the CAR algebra such that its fixed point algebra does not have the LP property.
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Qiu, Jianjun, and Yuqun Chen. "Free Lie differential Rota–Baxter algebras and Gröbner–Shirshov bases." International Journal of Algebra and Computation 27, no. 08 (December 2017): 1041–60. http://dx.doi.org/10.1142/s0218196717500485.

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Qiu, Jianjun. "Gröbner–Shirshov bases for commutative algebras with multiple operators and free commutative Rota–Baxter algebras." Asian-European Journal of Mathematics 07, no. 02 (June 2014): 1450033. http://dx.doi.org/10.1142/s1793557114500338.

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In this paper, the Composition-Diamond lemma for commutative algebras with multiple operators is established. As applications, the Gröbner–Shirshov bases and linear bases of free commutative Rota–Baxter algebra, free commutative λ-differential algebra and free commutative λ-differential Rota–Baxter algebra are given, respectively. Consequently, these three free algebras are constructed directly by commutative Ω-words.
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Gerrish, F., W. Keith Nicholson, and Harvey Gerber. "Elementary Linear Algebra, with Applications." Mathematical Gazette 75, no. 472 (June 1991): 230. http://dx.doi.org/10.2307/3620286.

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Dissertations / Theses on the topic "Application of linear algebra"

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Najahi, Mohamed amine. "Synthesis of certified programs in fixed-point arithmetic, and its application to linear algebra basic blocks : and its application to linear algebra basic blocks." Thesis, Perpignan, 2014. http://www.theses.fr/2014PERP1212.

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Pour réduire les coûts des systèmes embarqués, ces derniers sont livrés avec des micro-processeurs peu puissants. Ces processeurs sont dédiés à l'exécution de tâches calculatoires dont certaines, comme la transformée de Fourier rapide, peuvent s'avérer exigeantes en termes de ressources de calcul. Afin que les implémentations de ces algorithmes soient efficaces, les programmeurs utilisent l'arithmétique à virgule fixe qui est plus adaptée aux processeurs dépourvus d'unité flottante. Cependant, ils se retrouvent confrontés à deux difficultés: D'abord, coder en virgule fixe est fastidieux et exige que le programmeur gère tous les détails arithmétiques. Ensuite, et en raison de la faible dynamique des nombres à virgule fixe par rapport aux nombres flottants, les calculs en fixe sont souvent perçus comme intrinsèquement peu précis. La première partie de cette thèse propose une méthodologie pour dépasser ces deux limitations. Elle montre comment concevoir et mettre en œuvre des outils pour générer automatiquement des programmes en virgule fixe. Ensuite, afin de rassurer l'utilisateur quant à la qualité numérique des codes synthétisés, des certificats sont générés qui fournissent des bornes sur les erreurs d'arrondi. La deuxième partie de cette thèse est dédiée à l'étude des compromis lors de la génération de programmes en virgule fixe pour les briques d'algèbre linéaire. Des données expérimentales y sont fournies sur la synthèse de code pour la multiplication et l'inversion matricielles
To be cost effective, embedded systems are shipped with low-end micro-processors. These processors are dedicated to one or few tasks that are highly demanding on computational resources. Examples of widely deployed tasks include the fast Fourier transform, convolutions, and digital filters. For these tasks to run efficiently, embedded systems programmers favor fixed-point arithmetic over the standardized and costly floating-point arithmetic. However, they are faced with two difficulties: First, writing fixed-point codes is tedious and requires that the programmer must be in charge of every arithmetical detail. Second, because of the low dynamic range of fixed-point numbers compared to floating-point numbers, there is a persistent belief that fixed-point computations are inherently inaccurate. The first part of this thesis addresses these two limitations as follows: It shows how to design and implement tools to automatically synthesize fixed-point programs. Next, to strengthen the user's confidence in the synthesized codes, analytic methods are suggested to generate certificates. These certificates can be checked using a formal verification tool, and assert that the rounding errors of the generated codes are indeed below a given threshold. The second part of the thesis is a study of the trade-offs involved when generating fixed-point code for linear algebra basic blocks. It gives experimental data on fixed-point synthesis for matrix multiplication and matrix inversion through Cholesky decomposition
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Vasireddy, Jhansi Lakshmi. "Applications of Linear Algebra to Information Retrieval." Digital Archive @ GSU, 2009. http://digitalarchive.gsu.edu/math_theses/71.

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Some of the theory of nonnegative matrices is first presented. The Perron-Frobenius theorem is highlighted. Some of the important linear algebraic methods of information retrieval are surveyed. Latent Semantic Indexing (LSI), which uses the singular value de-composition is discussed. The Hyper-Text Induced Topic Search (HITS) algorithm is next considered; here the power method for finding dominant eigenvectors is employed. Through the use of a theorem by Sinkohrn and Knopp, a modified HITS method is developed. Lastly, the PageRank algorithm is discussed. Numerical examples and MATLAB programs are also provided.
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Perkins, Jonathan Hale. "Some applications of linear algebra to quantitative spectroscopy /." Thesis, Connect to this title online; UW restricted, 1988. http://hdl.handle.net/1773/11534.

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Poulson, Jack Lesly. "Formalized parallel dense linear algebra and its application to the generalized eigenvalue problem." Thesis, [Austin, Tex. : University of Texas, 2009. http://hdl.handle.net/2152/ETD-UT-2009-05-139.

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Sato, Hiroyuki. "Riemannian Optimization Algorithms and Their Applications to Numerical Linear Algebra." 京都大学 (Kyoto University), 2013. http://hdl.handle.net/2433/180615.

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Kanwar, Gurtej. "Linear algebra on lattices : Simit language extensions with applications to lattice QCD." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/105995.

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Thesis: M. Eng. in Computer Science and Engineering, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 155-160).
This thesis presents language extensions to Simit, a language for linear algebra on graphs. Currently, Simit doesn't efficiently handle lattice graphs (regular grids). This thesis defines a stencil assembly construct to capture linear algebra on these graphs. A prototype compiler with a Halide backend demonstrates that these extensions capture the full structure of linear algebra applications operating on lattices, are easily schedulable, and achieve comparable performance to existing methods. Many physical simulations take the form of linear algebra on lattices. This thesis reviews Lattice QCD as a representative example of such a class of applications and identifies the structure of the linear algebra involved. In this application, iterative inversion of the Dirac matrix dominates the runtime, and time-intensive hand-optimization of inverters for specific forms of the matrix limit further research. This thesis implements this computation using the language extensions, while demonstrating competitive performance to existing methods.
by Gurtej Kanwar.
M. Eng. in Computer Science and Engineering
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Torp, Audun. "Sparse linear algebra on a GPU : with Applications to flow in porous Media." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2009. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9044.

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We investigate what the graphics processing units (GPUs) have to offer compared to the central processing units (CPUs) when solving a sparse linear system of equations. This is performed by using a GPU to simulate fluid-flow in a porous medium. Flow-problems are discretized mainly by the mimetic finite element discretization, but also by a two-point flux-approximation (TPFA) method. Both of these discretization schemes are explained in detail. Example-models of flow in porous media are simulated, as well as CO2 -injection into a realistic model of a sub-sea storage-cite. The linear algebra is solved by the conjugate gradient (CG) method without a preconditioner. The computationally most expensive calculation of this algorithm is the matrix-vector product. Several formats for storing sparse matrices are presented and implemented on both a CPU and a GPU. The fastest format on the CPU is different from the format performing best on the GPU. Implementations for the GPU is written for the compute unified driver architecture (CUDA), and C++ is used for the CPU-implementations. The program is created as a plug-in for Matlab and may be used to solve any symmetric positive definite (SPD) linear system. How a GPU differs from a CPU is explained, where focus is put on how a program should be written to fully utilize the potential of a GPU. The optimized implementation on the GPU outperforms the CPU, and offers a substantial improvement compared to Matlab’s conjugate gradient method, when no preconditioner is used.

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Phillips, Adam. "GPU Accelerated Approach to Numerical Linear Algebra and Matrix Analysis with CFD Applications." Honors in the Major Thesis, University of Central Florida, 2014. http://digital.library.ucf.edu/cdm/ref/collection/ETH/id/1635.

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A GPU accelerated approach to numerical linear algebra and matrix analysis with CFD applications is presented. The works objectives are to (1) develop stable and efficient algorithms utilizing multiple NVIDIA GPUs with CUDA to accelerate common matrix computations, (2) optimize these algorithms through CPU/GPU memory allocation, GPU kernel development, CPU/GPU communication, data transfer and bandwidth control to (3) develop parallel CFD applications for Navier Stokes and Lattice Boltzmann analysis methods. Special consideration will be given to performing the linear algebra algorithms under certain matrix types (banded, dense, diagonal, sparse, symmetric and triangular). Benchmarks are performed for all analyses with baseline CPU times being determined to find speed-up factors and measure computational capability of the GPU accelerated algorithms. The GPU implemented algorithms used in this work along with the optimization techniques performed are measured against preexisting work and test matrices available in the NIST Matrix Market. CFD analysis looked to strengthen the assessment of this work by providing a direct engineering application to analysis that would benefit from matrix optimization techniques and accelerated algorithms. Overall, this work desired to develop optimization for selected linear algebra and matrix computations performed with modern GPU architectures and CUDA developer which were applied directly to mathematical and engineering applications through CFD analysis.
B.S.
Bachelors
Mathematics
Sciences
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Silva, Carlos Eduardo Vitória da. "Aplicações da álgebra linear nas cadeias de Markov." Universidade Federal de Goiás, 2013. http://repositorio.bc.ufg.br/tede/handle/tede/3480.

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Made available in DSpace on 2014-10-31T09:36:29Z (GMT). No. of bitstreams: 2 Dissertação - Carlos Eduardo Vitória da Silva - 2013.pdf: 1162244 bytes, checksum: d2966939f025f381680dcb9ce82d76ac (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-04-11
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
The theory of linear algebra and matrices and systems particularly are linear math topics that can be applied not only within mathematics itself, but also in various other areas of human knowledge, such as physics, chemistry, biology, all engineering, psychology, economy, transportation, administration, statistics and probability, etc... The Markov chains are used to solve certain problems in the theory of probability. Applications of Markov chains in these problems, depend directly on the theory of matrices and linear systems. In this work we use the techniques of Markov Chains to solve three problems of probability, in three distinct areas. One in genetics, other in psychology and the other in the area of mass transit in a transit system. All work is developed with the intention that a high school student can read and understand the solutions of three problems presented.
A teoria da álgebra linear e particularmente matrizes e sistemas lineares são tópicos de matemática que podem ser aplicados não só dentro da própria matemática, mas também em várias outras áreas do conhecimento humano, como física, química, biologia, todas as engenharias, psicologia, economia, transporte, administração, estat ística e probabilidade, etc. As Cadeias de Markov são usadas para resolver certos problemas dentro da teoria das probabilidades. As aplicações das Cadeias de Markov nesses problemas, dependem diretamente da teoria das matrizes e sistemas lineares. Neste trabalho usamos as técnicas das Cadeias de Markov para resolver três problemas de probabilidades, em três áreas distintas. Um na área da genética, outro na área da psicologia e o outro na área de transporte de massa em um sistema de trânsito. Todo o trabalho é desenvolvido com a intenção de que um estudante do ensino médio possa ler e entender as soluções dos três problemas apresentados.
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Frazier, William. "Application of Symplectic Integration on a Dynamical System." Digital Commons @ East Tennessee State University, 2017. https://dc.etsu.edu/etd/3213.

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Molecular Dynamics (MD) is the numerical simulation of a large system of interacting molecules, and one of the key components of a MD simulation is the numerical estimation of the solutions to a system of nonlinear differential equations. Such systems are very sensitive to discretization and round-off error, and correspondingly, standard techniques such as Runge-Kutta methods can lead to poor results. However, MD systems are conservative, which means that we can use Hamiltonian mechanics and symplectic transformations (also known as canonical transformations) in analyzing and approximating solutions. This is standard in MD applications, leading to numerical techniques known as symplectic integrators, and often, these techniques are developed for well-understood Hamiltonian systems such as Hill’s lunar equation. In this presentation, we explore how well symplectic techniques developed for well-understood systems (specifically, Hill’s Lunar equation) address discretization errors in MD systems which fail for one or more reasons.
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Books on the topic "Application of linear algebra"

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Bretscher, Otto. Linear algebra with applications. Upper Saddle River, N.J: Prentice Hall, 1997.

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Bretscher, Otto. Linear algebra with applications. 4th ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2009.

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Bretscher, Otto. Linear algebra with applications. 2nd ed. Upper Saddle River, NJ: Prentice Hall, 2001.

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Linear algebra with applications. 5th ed. Upper Saddle River, NJ: Prentice Hall, 2005.

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Linear algebra: Ideas and applications. 3rd ed. Hoboken, N.J: Wiley, 2008.

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Penney, Richard C. Linear algebra: Ideas and applications. New York: J. Wiley, 1998.

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Linear algebra: Ideas and applications. 2nd ed. Hoboken, N.J: Wiley-Interscience, 2004.

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Linear algebra: Ideas and applications. Hoboken, New Jersey: John Wiley & Sons, Inc., 2015.

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Chris, Rorres, ed. Elementary linear algebra: Applications version. 9th ed. New York: Wiley, 2005.

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Anton, Howard. Elementary linear algebra: Applications version. 6th ed. New York: John Wiley, 1991.

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Book chapters on the topic "Application of linear algebra"

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Smith, Larry. "Application to Differential Equations." In Linear Algebra, 381–404. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1670-4_18.

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Scaglia, Gustavo, Mario Emanuel Serrano, and Pedro Albertos. "Application to Industrial Processes." In Linear Algebra Based Controllers, 85–102. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-42818-1_6.

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Betounes, David. "Linear Algebra." In Differential Equations: Theory and Applications, 579–611. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-1-4419-1163-6_12.

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Scaglia, Gustavo, Mario Emanuel Serrano, and Pedro Albertos. "Application to a Mobile Robot." In Linear Algebra Based Controllers, 23–32. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-42818-1_3.

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Smith, Larry. "Linear Transformations: Examples and Applications." In Linear Algebra, 113–28. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1670-4_9.

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Scaglia, Gustavo, Mario Emanuel Serrano, and Pedro Albertos. "Application to Marine and Aerial Vehicles." In Linear Algebra Based Controllers, 55–84. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-42818-1_5.

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Gopi, E. S. "Linear Algebra." In Mathematical Summary for Digital Signal Processing Applications with Matlab, 153–79. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-3747-3_4.

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Heck, André. "Linear Algebra: Applications." In Introduction to Maple, 601–34. New York, NY: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4684-0484-5_19.

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Heck, André. "Linear Algebra: Applications." In Introduction to Maple, 435–67. New York, NY: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4684-0519-4_18.

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Heck, André. "Linear Algebra: Applications." In Introduction to Maple, 663–96. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/978-1-4613-0023-6_19.

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Conference papers on the topic "Application of linear algebra"

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Kunzinger, M. "Recent progress in special Colombeau algebras: geometry, topology, and algebra." In Linear and Non-Linear Theory of Generalized Functions and its Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2010. http://dx.doi.org/10.4064/bc88-0-14.

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Jin, Lihong, Chongrong Bi, and Yi'nan Zhao. "Application of MATLAB Software for Linear Algebra." In 2011 Third Pacific-Asia Conference on Circuits, Communications and System (PACCS). IEEE, 2011. http://dx.doi.org/10.1109/paccs.2011.5990256.

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Wu, Wenyuan, and Greg Reid. "Application of numerical algebraic geometry and numerical linear algebra to PDE." In the 2006 international symposium. New York, New York, USA: ACM Press, 2006. http://dx.doi.org/10.1145/1145768.1145824.

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Rahim, Rini Hafzah Abdul, Siti Hasnah Tanalol, Rozita Ismail, Aslina Baharum, Emelia Abdul Rahim, and Noorsidi Aizuddin Mat Noor. "Development of Gamification Linear Algebra Application Using Storytelling." In 2019 International Conference on Information and Communication Technology Convergence (ICTC). IEEE, 2019. http://dx.doi.org/10.1109/ictc46691.2019.8939953.

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Skalicky, Sam, Sonia Lopez, Marcin Lukowiak, James Letendre, and David Gasser. "Linear algebra computations in heterogeneous systems." In 2013 IEEE 24th International Conference on Application-specific Systems, Architectures and Processors (ASAP). IEEE, 2013. http://dx.doi.org/10.1109/asap.2013.6567589.

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Valley, George C., Thomas J. Shaw, Andrew D. Stapleton, Adam C. Scofield, George A. Sefler, and Leif Johannson. "Application of laser speckle to randomized numerical linear algebra." In Optical Data Science: Trends Shaping the Future of Photonics, edited by Ken-ichi Kitayama, Bahram Jalali, and Ata Mahjoubfar. SPIE, 2018. http://dx.doi.org/10.1117/12.2294574.

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Zekraoui, Hanifa. "A Note on Application of Linear Algebra in Biology." In IBRAS 2021 INTERNATIONAL CONFERENCE ON BIOLOGICAL RESEARCH AND APPLIED SCIENCE. Juw, 2021. http://dx.doi.org/10.37962/ibras/2021/155.

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Tinnirello, Alicia María, Eduardo Alberto Gago, and Paola Andrea Szekieta. "ALGORITHMIC MATHEMATICS IN LINEAR ALGEBRA APPLICATIONS." In 12th International Technology, Education and Development Conference. IATED, 2018. http://dx.doi.org/10.21125/inted.2018.1738.

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Howard, Marylesa. "Linear Algebra Applications in National Security." In Society for Industrial and Applied Mathematics (SIAM) VIRTUAL Conference on Applied Linear Algebra 2021, May 17-21, 2021. https://www.siam.org/conferences/cm/conference/la21. US DOE, 2021. http://dx.doi.org/10.2172/1782691.

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Brunie, Nicolas. "Towards the Basic Linear Algebra Unit : Replicating multi-dimensional FPUs to accelerate linear algebra applications." In 2020 54th Asilomar Conference on Signals, Systems, and Computers. IEEE, 2020. http://dx.doi.org/10.1109/ieeeconf51394.2020.9443541.

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Reports on the topic "Application of linear algebra"

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Kamen, Edward W. Control of Linear Systems Over Commutative Normed Algebras with Applications. Fort Belvoir, VA: Defense Technical Information Center, February 1987. http://dx.doi.org/10.21236/ada178765.

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Bradley, John S. Special Year on Numerical Linear Algebra. Fort Belvoir, VA: Defense Technical Information Center, September 1988. http://dx.doi.org/10.21236/ada208199.

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Swetz, Frank. Review ofThe Chinese Roots of Linear Algebra. Washington, DC: The MAA Mathematical Sciences Digital Library, February 2011. http://dx.doi.org/10.4169/loci003627.

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Anuta, M. A., D. W. Lozier, N. Schabanel, and P. R. Turner. Basic linear algebra operations in SLI arithmetic. Gaithersburg, MD: National Institute of Standards and Technology, 1996. http://dx.doi.org/10.6028/nist.ir.5811.

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Freund, R. F. Linear Algebra on a CRAY X-MP. Fort Belvoir, VA: Defense Technical Information Center, April 1990. http://dx.doi.org/10.21236/ada221780.

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Carson, E. Final Report: Mixed Precision Numerical Linear Algebra. Office of Scientific and Technical Information (OSTI), June 2021. http://dx.doi.org/10.2172/1798446.

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Dongarra, J. J., R. van de Geijn, and D. W. Walker. A look at scalable dense linear algebra libraries. Office of Scientific and Technical Information (OSTI), July 1992. http://dx.doi.org/10.2172/10164371.

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Dongarra, J. J., R. van de Geijn, and D. W. Walker. A look at scalable dense linear algebra libraries. Office of Scientific and Technical Information (OSTI), July 1992. http://dx.doi.org/10.2172/7275582.

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Heroux, Michael Allen, and Bryan Marker. LDRD final report : autotuning for scalable linear algebra. Office of Scientific and Technical Information (OSTI), September 2011. http://dx.doi.org/10.2172/1029773.

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Georganas, Evangelos, Jorge Gonzalez-Dominguez, Edgar Solomonik, Yili Zheng, Juan Tourino, and Katherine A. Yelick. Communication Avoiding and Overlapping for Numerical Linear Algebra. Fort Belvoir, VA: Defense Technical Information Center, May 2012. http://dx.doi.org/10.21236/ada561679.

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