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Готові списки джерел за темами / Numerical linear and multilinear algebra

Добірка наукової літератури з теми "Numerical linear and multilinear algebra"

Автор: Grafiati

Опубліковано: 18 травня 2024

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Статті в журналах з теми "Numerical linear and multilinear algebra"

1

Bini, Dario, Marilena Mitrouli, Marc Van Barel, and Joab Winkler. "Structured Numerical Linear and Multilinear Algebra: Analysis, Algorithms and Applications." Linear Algebra and its Applications 502 (August 2016): 1–4. http://dx.doi.org/10.1016/j.laa.2016.03.042.

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2

Huang, Zhengge, and Jingjing Cui. "Improved Brauer-type eigenvalue localization sets for tensors with their applications." Filomat 34, no. 14 (2020): 4607–25. http://dx.doi.org/10.2298/fil2014607h.

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In this paper, by excluding some sets from the Brauer-type eigenvalue inclusion sets for tensors developed by Bu et al. (Linear Algebra Appl. 512 (2017) 234-248) and Li et al. (Linear and Multilinear Algebra 64 (2016) 727-736), some improved Brauer-type eigenvalue localization sets for tensors are given, which are proved to be much tighter than those put forward by Bu et al. and Li et al. As applications, some new criteria for identifying the nonsingularity of tensors are developed, which are better than some previous results. This fact is illustrated by some numerical examples.

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3

Sahoo, Satyajit. "On A-numerical radius inequalities for 2 x 2 operator matrices-II." Filomat 35, no. 15 (2021): 5237–52. http://dx.doi.org/10.2298/fil2115237s.

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Rout et al. [Linear Multilinear Algebra 2020, DOI: 10.1080/03081087.2020.1810201] presented certain A-numerical radius inequalities for 2x2 operator matrices and further results on A-numerical radius of certain 2x2 operator matrices are obtained by Feki [Hacet. J. Math. Stat., 2020, DOI:10.15672/hujms.730574], very recently. The main goal of this article is to establish certain A-numerical radius equalities for operator matrices. Several new upper and lower bounds for the A-numerical radius of 2 x 2 operator matrices has been proved, where A be the 2 x 2 diagonal operator matrix whose diagonal entries are positive bounded operator A. Further, we prove some refinements of earlier A-numerical radius inequalities for operators.

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4

Khoromskij, B. N. "Structured Rank-(r1, . . . , rd) Decomposition of Function-related Tensors in R_D." Computational Methods in Applied Mathematics 6, no. 2 (2006): 194–220. http://dx.doi.org/10.2478/cmam-2006-0010.

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AbstractThe structured tensor-product approximation of multidimensional nonlocal operators by a two-level rank-(r1, . . . , rd) decomposition of related higher-order tensors is proposed and analysed. In this approach, the construction of the desired approximant to a target tensor is a reminiscence of the Tucker-type model, where the canonical components are represented in a fixed (uniform) basis, while the core tensor is given in the canonical format. As an alternative, the multilevel nested canonical decomposition is presented. The complexity analysis of the corresponding multilinear algebra shows an almost linear cost in the one-dimensional problem size. The existence of a low Kronecker rank two-level representation is proven for a class of function-related tensors.

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5

Benzi, Michele, and Ru Huang. "Some matrix properties preserved by generalized matrix functions." Special Matrices 7, no. 1 (January 8, 2019): 27–37. http://dx.doi.org/10.1515/spma-2019-0003.

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Abstract Generalized matrix functions were first introduced in [J. B. Hawkins and A. Ben-Israel, Linear and Multilinear Algebra, 1(2), 1973, pp. 163-171]. Recently, it has been recognized that these matrix functions arise in a number of applications, and various numerical methods have been proposed for their computation. The exploitation of structural properties, when present, can lead to more efficient and accurate algorithms. The main goal of this paper is to identify structural properties of matrices which are preserved by generalized matrix functions. In cases where a given property is not preserved in general, we provide conditions on the underlying scalar function under which the property of interest will be preserved by the corresponding generalized matrix function.

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6

Choi, Yun Sung, Domingo Garcia, Sung Guen Kim, and Manuel Maestre. "THE POLYNOMIAL NUMERICAL INDEX OF A BANACH SPACE." Proceedings of the Edinburgh Mathematical Society 49, no. 1 (February 2006): 39–52. http://dx.doi.org/10.1017/s0013091502000810.

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AbstractIn this paper, we introduce the polynomial numerical index of order $k$ of a Banach space, generalizing to $k$-homogeneous polynomials the ‘classical’ numerical index defined by Lumer in the 1970s for linear operators. We also prove some results. Let $k$ be a positive integer. We then have the following:(i) $n^{(k)}(C(K))=1$ for every scattered compact space $K$.(ii) The inequality $n^{(k)}(E)\geq k^{k/(1-k)}$ for every complex Banach space $E$ and the constant $k^{k/(1-k)}$ is sharp.(iii) The inequalities$$ n^{(k)}(E)\leq n^{(k-1)}(E)\leq\frac{k^{(k+(1/(k-1)))}}{(k-1)^{k-1}}n^{(k)}(E) $$for every Banach space $E$.(iv) The relation between the polynomial numerical index of $c_0$, $l_1$, $l_{\infty}$ sums of Banach spaces and the infimum of the polynomial numerical indices of them.(v) The relation between the polynomial numerical index of the space $C(K,E)$ and the polynomial numerical index of $E$.(vi) The inequality $n^{(k)}(E^{**})\leq n^{(k)}(E)$ for every Banach space $E$.Finally, some results about the numerical radius of multilinear maps and homogeneous polynomials on $C(K)$ and the disc algebra are given.

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7

Qi, Liqun, Yimin Wei, Changqing Xu, and Tan Zhang. "Linear algebra and multilinear algebra." Frontiers of Mathematics in China 11, no. 3 (May 6, 2016): 509–10. http://dx.doi.org/10.1007/s11464-016-0540-0.

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8

Marcus, Marvin. "Multilinear methods in linear algebra." Linear Algebra and its Applications 150 (May 1991): 41–59. http://dx.doi.org/10.1016/0024-3795(91)90158-s.

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9

Qi, Liqun, Wenyu Sun, and Yiju Wang. "Numerical multilinear algebra and its applications." Frontiers of Mathematics in China 2, no. 4 (October 2007): 501–26. http://dx.doi.org/10.1007/s11464-007-0031-4.

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10

Gentle, James. "Matrix Analysis and Applied Linear Algebra, Numerical Linear Algebra, and Applied Numerical Linear Algebra." Journal of the American Statistical Association 96, no. 455 (September 2001): 1136–37. http://dx.doi.org/10.1198/jasa.2001.s412.

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Дисертації з теми "Numerical linear and multilinear algebra"

1

Waldherr, Konrad [Verfasser]. "Numerical Linear and Multilinear Algebra in Quantum Control and Quantum Tensor Networks / Konrad Waldherr." München : Verlag Dr. Hut, 2014. http://d-nb.info/1064560601/34.

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2

Lim, Lek-Heng. "Foundations of numerical multilinear algebra : decomposition and approximation of tensors /." May be available electronically:, 2007. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.

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3

Battles, Zachary. "Numerical linear algebra for continuous functions." Thesis, University of Oxford, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.427900.

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4

Higham, N. J. "Nearness problems in numerical linear algebra." Thesis, University of Manchester, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.374580.

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5

Zounon, Mawussi. "On numerical resilience in linear algebra." Thesis, Bordeaux, 2015. http://www.theses.fr/2015BORD0038/document.

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Comme la puissance de calcul des systèmes de calcul haute performance continue de croître, en utilisant un grand nombre de cœurs CPU ou d’unités de calcul spécialisées, les applications hautes performances destinées à la résolution des problèmes de très grande échelle sont de plus en plus sujettes à des pannes. En conséquence, la communauté de calcul haute performance a proposé de nombreuses contributions pour concevoir des applications tolérantes aux pannes. Cette étude porte sur une nouvelle classe d’algorithmes numériques de tolérance aux pannes au niveau de l’application qui ne nécessite pas de ressources supplémentaires, à savoir, des unités de calcul ou du temps de calcul additionnel, en l’absence de pannes. En supposant qu’un mécanisme distinct assure la détection des pannes, nous proposons des algorithmes numériques pour extraire des informations pertinentes à partir des données disponibles après une pannes. Après l’extraction de données, les données critiques manquantes sont régénérées grâce à des stratégies d’interpolation pour constituer des informations pertinentes pour redémarrer numériquement l’algorithme. Nous avons conçu ces méthodes appelées techniques d’Interpolation-restart pour des problèmes d’algèbre linéaire numérique tels que la résolution de systèmes linéaires ou des problèmes aux valeurs propres qui sont indispensables dans de nombreux noyaux scientifiques et applications d’ingénierie. La résolution de ces problèmes est souvent la partie dominante; en termes de temps de calcul, des applications scientifiques. Dans le cadre solveurs linéaires du sous-espace de Krylov, les entrées perdues de l’itération sont interpolées en utilisant les entrées disponibles sur les nœuds encore disponibles pour définir une nouvelle estimation de la solution initiale avant de redémarrer la méthode de Krylov. En particulier, nous considérons deux politiques d’interpolation qui préservent les propriétés numériques clés de solveurs linéaires bien connus, à savoir la décroissance monotone de la norme-A de l’erreur du gradient conjugué ou la décroissance monotone de la norme résiduelle de GMRES. Nous avons évalué l’impact du taux de pannes et l’impact de la quantité de données perdues sur la robustesse des stratégies de résilience conçues. Les expériences ont montré que nos stratégies numériques sont robustes même en présence de grandes fréquences de pannes, et de perte de grand volume de données. Dans le but de concevoir des solveurs résilients de résolution de problèmes aux valeurs propres, nous avons modifié les stratégies d’interpolation conçues pour les systèmes linéaires. Nous avons revisité les méthodes itératives de l’état de l’art pour la résolution des problèmes de valeurs propres creux à la lumière des stratégies d’Interpolation-restart. Pour chaque méthode considérée, nous avons adapté les stratégies d’Interpolation-restart pour régénérer autant d’informations spectrale que possible. Afin d’évaluer la performance de nos stratégies numériques, nous avons considéré un solveur parallèle hybride (direct/itérative) pleinement fonctionnel nommé MaPHyS pour la résolution des systèmes linéaires creux, et nous proposons des solutions numériques pour concevoir une version tolérante aux pannes du solveur. Le solveur étant hybride, nous nous concentrons dans cette étude sur l’étape de résolution itérative, qui est souvent l’étape dominante dans la pratique. Les solutions numériques proposées comportent deux volets. A chaque fois que cela est possible, nous exploitons la redondance de données entre les processus du solveur pour effectuer une régénération exacte des données en faisant des copies astucieuses dans les processus. D’autre part, les données perdues qui ne sont plus disponibles sur aucun processus sont régénérées grâce à un mécanisme d’interpolation
As the computational power of high performance computing (HPC) systems continues to increase by using huge number of cores or specialized processing units, HPC applications are increasingly prone to faults. This study covers a new class of numerical fault tolerance algorithms at application level that does not require extra resources, i.e., computational unit or computing time, when no fault occurs. Assuming that a separate mechanism ensures fault detection, we propose numerical algorithms to extract relevant information from available data after a fault. After data extraction, well chosen part of missing data is regenerated through interpolation strategies to constitute meaningful inputs to numerically restart the algorithm. We have designed these methods called Interpolation-restart techniques for numerical linear algebra problems such as the solution of linear systems or eigen-problems that are the inner most numerical kernels in many scientific and engineering applications and also often ones of the most time consuming parts. In the framework of Krylov subspace linear solvers the lost entries of the iterate are interpolated using the available entries on the still alive nodes to define a new initial guess before restarting the Krylov method. In particular, we consider two interpolation policies that preserve key numerical properties of well-known linear solvers, namely the monotony decrease of the A-norm of the error of the conjugate gradient or the residual norm decrease of GMRES. We assess the impact of the fault rate and the amount of lost data on the robustness of the resulting linear solvers.For eigensolvers, we revisited state-of-the-art methods for solving large sparse eigenvalue problems namely the Arnoldi methods, subspace iteration methods and the Jacobi-Davidson method, in the light of Interpolation-restart strategies. For each considered eigensolver, we adapted the Interpolation-restart strategies to regenerate as much spectral information as possible. Through intensive experiments, we illustrate the qualitative numerical behavior of the resulting schemes when the number of faults and the amount of lost data are varied; and we demonstrate that they exhibit a numerical robustness close to that of fault-free calculations. In order to assess the efficiency of our numerical strategies, we have consideredan actual fully-featured parallel sparse hybrid (direct/iterative) linear solver, MaPHyS, and we proposed numerical remedies to design a resilient version of the solver. The solver being hybrid, we focus in this study on the iterative solution step, which is often the dominant step in practice. The numerical remedies we propose are twofold. Whenever possible, we exploit the natural data redundancy between processes from the solver toperform an exact recovery through clever copies over processes. Otherwise, data that has been lost and is not available anymore on any process is recovered through Interpolationrestart strategies. These numerical remedies have been implemented in the MaPHyS parallel solver so that we can assess their efficiency on a large number of processing units (up to 12; 288 CPU cores) for solving large-scale real-life problems

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6

Kannan, Ramaseshan. "Numerical linear algebra problems in structural analysis." Thesis, University of Manchester, 2014. https://www.research.manchester.ac.uk/portal/en/theses/numerical-linear-algebra-problems-in-structural-analysis(7df0f708-fc12-4807-a1f5-215960d9c4d4).html.

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A range of numerical linear algebra problems that arise in finite element-based structural analysis are considered. These problems were encountered when implementing the finite element method in the software package Oasys GSA. We present novel solutions to these problems in the form of a new method for error detection, algorithms with superior numerical effeciency and algorithms with scalable performance on parallel computers. The solutions and their corresponding software implementations have been integrated into GSA's program code and we present results that demonstrate the use of these implementations by engineers to solve real-world structural analysis problems.

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7

Steele, Hugh Paul. "Combinatorial arguments for linear logic full completeness." Thesis, University of Manchester, 2013. https://www.research.manchester.ac.uk/portal/en/theses/combinatorial-arguments-for-linear-logic-full-completeness(274c6b87-dc58-4dc3-86bc-8c29abc2fc34).html.

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We investigate categorical models of the unit-free multiplicative and multiplicative-additive fragments of linear logic by representing derivations as particular structures known as dinatural transformations. Suitable categories are considered to satisfy a property known as full completeness if all such entities are the interpretation of a correct derivation. It is demonstrated that certain Hyland-Schalk double glueings [HS03] are capable of transforming large numbers of degenerate models into more accurate ones. Compact closed categories with finite biproducts possess enough structure that their morphisms can be described as forms of linear arrays. We introduce the notion of an extended tensor (or ‘extensor’) over arbitrary semirings, and show that they uniquely describe arrows between objects generated freely from the tensor unit in such categories. It is made evident that the concept may be extended yet further to provide meaningful decompositions of more general arrows. We demonstrate how the calculus of extensors makes it possible to examine the combinatorics of certain double glueing constructions. From this we show that the Hyland-Tan version [Tan97], when applied to compact closed categories satisfying a far weaker version of full completeness, produces genuine fully complete models of unit-free multiplicative linear logic. Research towards the development of a full completeness result for the multiplicative-additive fragment is detailed. The proofs work for categories of finite arrays over certain semirings under both the Hyland-Tan and Schalk [Sch04] constructions. We offer a possible route to finishing this proof. An interpretation of these results with respect to linear logic proof theory is provided, and possible further research paths and generalisations are discussed.

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8

Gulliksson, Rebecka. "A comparison of parallelization approaches for numerical linear algebra." Thesis, Umeå universitet, Institutionen för datavetenskap, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-81116.

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The efficiency of numerical libraries for a given computation is highly dependent on the size of the inputs. For very small inputs it is expected that LAPACK combined with BLAS is the superior alternative, while the new generation of parallelized numerical libraries (such as PLASMA and SuperMatrix) is expected to be superior for large inputs. In between these two extremes in input sizes, there might exist a niche for a new class of numerical libraries.In this thesis a prototype library, targeting medium sized inputs, is presented. The prototype library uses a mixed data and task parallel approach, with the Static BFS Scheduling of M-tasks (SBSM) algorithm, and provides lightweight scheduling for numerical computations. The aim of the prototype library is to explore the competitiveness of such an approach, compared to the more traditional parallelization approaches (data and task parallelism). The competitiveness is measured in a set of synthetic benchmarks using matrix multiplication as the reference computation.The results show that the prototype library exhibits potential for superseding the performance of today’s libraries for medium sized inputs. To give a conclusive answer as to whether the approach is worth pursuing with large research and development efforts, further investigation of the scheduling algorithm, as well as the numerical computations, should be examined through additional benchmarks.

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9

Song, Zixu. "Software engineering abstractions for a numerical linear algebra library." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/software-engineering-abstractions-for-a-numerical-linear-algebra-library(68304a9b-56db-404b-8ffb-4613f5102c1a).html.

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This thesis aims at building a numerical linear algebra library with appropriate software engineering abstractions. Three areas of knowledge, namely, Numerical Linear Algebra (NLA), Software Engineering and Compiler Optimisation Techniques, are involved. Numerical simulation is widely used in a large number of distinct disciplines to help scientists understand and discover the world. The solutions to frequently occurring numerical problems have been implemented in subroutines, which were then grouped together to form libraries for ease of use. The design, implementation and maintenance of a NLA library require a great deal of work so that the other two topics, namely, software engineering and compiler optimisation techniques have emerged. Generally speaking, these both try to divide the system into smaller and controllable concerns, and allow the programmer to deal with fewer concerns at one time. Band matrix operation, as a new level of abstraction, is proposed for simplifying library implementation and enhancing extensibility for future functionality upgrades. Iteration Space Partitioning (ISP) is applied, in order to make the performance of this generalised implementation for band matrices comparable to that of the specialised implementations for dense and triangular matrices. The optimisation of ISP can be either programmed using the pointcut-advice model of Aspect-Oriented Programming, or integrated as part of a compiler. This naturally leads to a comparison of these two different techniques for resolving one fundamental problem. The thesis shows that software engineering properties of a library, such as modularity and extensibility, can be improved by the use of the appropriate level of abstraction, while performance is either not sacrificed at all, or at least the loss of performance is limited. In other words, the perceived trade-off between the use of high-level abstraction and fast execution is made less significant than previously assumed.

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10

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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Книги з теми "Numerical linear and multilinear algebra"

1

service), SpringerLink (Online, ed. The Linear Algebra a Beginning Graduate Student Ought to Know. 3rd ed. Dordrecht: Springer Netherlands, 2012.

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2

Multilinear algebra. Amsterdam: Gordon and Breach Science Publishers, 1997.

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3

Numerical linear algebra. New York, NY: Springer, 2008.

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4

Reichel, Lothar, Arden Ruttan, and Richard S. Varga, eds. Numerical Linear Algebra. Berlin, New York: DE GRUYTER, 1993. http://dx.doi.org/10.1515/9783110857658.

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5

Allaire, Grégoire, and Sidi Mahmoud Kaber. Numerical Linear Algebra. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-68918-0.

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6

Bornemann, Folkmar. Numerical Linear Algebra. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74222-9.

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7

David, Bau, ed. Numerical linear algebra. Philadelphia: Society for Industrial and Applied Mathematics, 1997.

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8

O, Christenson Charles, and Smith Bryan A, eds. Numerical linear algebra. Moscow, Idaho: BCS Associates, 1991.

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9

Bourhim, A., J. Mashreghi, L. Oubbi, and Z. Abdelali, eds. Linear and Multilinear Algebra and Function Spaces. Providence, Rhode Island: American Mathematical Society, 2020. http://dx.doi.org/10.1090/conm/750.

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10

Petersen, Peter. Linear Algebra. New York, NY: Springer New York, 2012.

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Частини книг з теми "Numerical linear and multilinear algebra"

1

Bourbaki, Nicolas. "Linear Algebra and Multilinear Algebra." In Elements of the History of Mathematics, 57–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-61693-8_4.

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2

Bullo, Francesco, and Andrew D. Lewis. "Linear and multilinear algebra." In Texts in Applied Mathematics, 15–48. New York, NY: Springer New York, 2005. http://dx.doi.org/10.1007/978-1-4899-7276-7_2.

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3

Hestenes, David, and Garret Sobczyk. "Linear and Multilinear Functions." In Clifford Algebra to Geometric Calculus, 63–136. Dordrecht: Springer Netherlands, 1987. http://dx.doi.org/10.1007/978-94-009-6292-7_3.

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4

Loehr, Nicholas A. "Universal Mapping Problems in Multilinear Algebra." In Advanced Linear Algebra, 571–606. 2nd ed. Boca Raton: Chapman and Hall/CRC, 2024. http://dx.doi.org/10.1201/9781003484561-20.

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5

Serre, Denis. "Elementary Linear and Multilinear Algebra." In Graduate Texts in Mathematics, 1–14. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-7683-3_1.

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6

Li, PhD, Haksun. "Linear Algebra." In Numerical Methods Using Kotlin, 35–139. Berkeley, CA: Apress, 2022. http://dx.doi.org/10.1007/978-1-4842-8826-9_2.

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7

Li, PhD, Haksun. "Linear Algebra." In Numerical Methods Using Java, 71–206. Berkeley, CA: Apress, 2022. http://dx.doi.org/10.1007/978-1-4842-6797-4_2.

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8

Robbiano, Lorenzo. "Numerical and Symbolic Computations." In Linear algebra, 1–6. Milano: Springer Milan, 2011. http://dx.doi.org/10.1007/978-88-470-1839-6_1.

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9

Gentle, James E. "Numerical Linear Algebra." In Springer Texts in Statistics, 523–38. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-64867-5_11.

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10

Čížková, Lenka, and Pavel Čížek. "Numerical Linear Algebra." In Handbook of Computational Statistics, 105–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-21551-3_5.

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Тези доповідей конференцій з теми "Numerical linear and multilinear algebra"

1

Clarkson, Kenneth L., and David P. Woodruff. "Numerical linear algebra in the streaming model." In the 41st annual ACM symposium. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1536414.1536445.

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2

Ammar, Gregory. "Grassmannians, Riccati equations, and numerical linear algebra." In 1985 24th IEEE Conference on Decision and Control. IEEE, 1985. http://dx.doi.org/10.1109/cdc.1985.268867.

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3

Meier, Ulrike, and Ahmed Sameh. "Numerical Linear Algebra On The CEDAR Multiprocessor." In 31st Annual Technical Symposium, edited by Franklin T. Luk. SPIE, 1988. http://dx.doi.org/10.1117/12.942008.

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Václavíková, Zuzana, and Ondřej Kolouch. "Linear algebra for students of informatics." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0027086.

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5

Krake, Tim. "Numerical Linear Algebra for physically-based Fluid Animations." In SA '19: SIGGRAPH Asia 2019. New York, NY, USA: ACM, 2019. http://dx.doi.org/10.1145/3366344.3366445.

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6

Georganas, Evangelos, Jorge Gonzalez-Dominguez, Edgar Solomonik, Yili Zheng, Juan Tourino, and Katherine Yelick. "Communication avoiding and overlapping for numerical linear algebra." In 2012 SC - International Conference for High Performance Computing, Networking, Storage and Analysis. IEEE, 2012. http://dx.doi.org/10.1109/sc.2012.32.

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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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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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Hu, Dong, Shashanka Ubaru, Alex Gittens, Kenneth L. Clarkson, Lior Horesh, and Vassilis Kalantzis. "Sparse Graph Based Sketching for Fast Numerical Linear Algebra." In ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2021. http://dx.doi.org/10.1109/icassp39728.2021.9414030.

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Krüger, Jens, and Rüdiger Westermann. "Linear algebra operators for GPU implementation of numerical algorithms." In ACM SIGGRAPH 2005 Courses. New York, New York, USA: ACM Press, 2005. http://dx.doi.org/10.1145/1198555.1198795.

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Звіти організацій з теми "Numerical linear and multilinear algebra"

1

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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2

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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3

Carson, E. Final Report: Mixed Precision Numerical Linear Algebra. Office of Scientific and Technical Information (OSTI), June 2022. http://dx.doi.org/10.2172/1872699.

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4

Carson, E. Final Report: Mixed Precision Numerical Linear Algebra. Office of Scientific and Technical Information (OSTI), October 2023. http://dx.doi.org/10.2172/2204467.

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Carson, E. Final Report: Mixed Precision Numerical Linear Algebra. Office of Scientific and Technical Information (OSTI), December 2023. http://dx.doi.org/10.2172/2280470.

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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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Vu, Van H. Random Matrices, Combinatorics, Numerical Linear Algebra and Complex Networks. Fort Belvoir, VA: Defense Technical Information Center, February 2012. http://dx.doi.org/10.21236/ada567088.

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Demmel, James. Conference: Three Decades of Numerical Linear Algebra at Berkeley. Fort Belvoir, VA: Defense Technical Information Center, April 1993. http://dx.doi.org/10.21236/ada264964.

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