Extending Ginkgo to Manage Reconfigurable Hardware-Based Kernels by Alejandro Morales-Peña, Esteban Meneses

“… Although heterogeneous systems based on hardware accelerators are a trending topic in the HPC community, exploring the trade-offs of reconfigurable hardware-based ones in linear algebra libraries for high-performance systems, has not been deeply studied. …”
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CLOUD SERVICES FOR ORGANIZATION OF STUDENTS’ EDUCATION ACTIVITY CONTROL by Olesya M. Abramova

“…The article dwellson thequestions ofa choice and theuse of innovative technologies forcontrol of education activity of futureeconomists when studyingdiscipline «Linear algebra». The article discuss the methodical possibilities of cloud services that functionally are the most suitable for the organization of educational activity control in the modern educational environment. …”
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A Framework for Coxeter Spectral Classification of Finite Posets and Their Mesh Geometries of Roots by Daniel Simson, Katarzyna Zając

“…Following our paper [Linear Algebra Appl. 433(2010), 699–717], we present a framework and computational tools for the Coxeter spectral classification of finite posets J≡(J,⪯). …”
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A Geometric Property of the Laplacian matrix of a Connected Nonsingular Mixed Graph by Zheng-Da Zhou, Shi-Cai Gong

“…Fiedler, Geometry of the Laplacian, Linear Algebra Appl., 2005, 403: 409–413). In addition, the relations of geometric properties between a connected (singular or nonsingular) mixed graph, and all its resigned graphs will be characterized.…”
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Primary decomposition of torsion R[X]-modules by William A. Adkins

“…This is a generalization of the classical fact from linear algebra that a diagonalizable linear transformation on a vector space restricts to a diagonalizable linear transformation of any invariant subspace. …”
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Thermodynamic matrix exponentials and thermodynamic parallelism by Samuel Duffield, Maxwell Aifer, Gavin Crooks, Thomas Ahle, Patrick J. Coles

“…It was recently shown that certain linear algebra problems can be solved thermodynamically, leading to a speedup scaling with the matrix dimension. …”
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Aspects of using computer programs in teaching higher mathematics at university by Ekaterina V. Mazurenko

“…The possibility of using mathematical software in the study of linear algebra by first-year students of a technical university is justified.…”
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Complexity of Some Generalized Operations on Networks by Muhammad Javaid, Hafiz Usman Afzal, Shaohui Wang

“…All our findings in this article have been obtained by applying the methods from linear algebra, matrix theory, and Chebyshev polynomials. …”
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Usage of computer algebra in teaching process by Aleksas Domarkas, Gintautas Misevičius, Violeta Pakalnytė, Albertas Pincevičius, Rimantas-Jonas Rakauskas

“…Namely, it is the problems of linear algebra, analyse of graphs, numerical calculation, integration, solution of differential equations, statistics for management, linear programming. …”
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Comparison of Gaussian Elimination and Cholesky Decomposition Solving A Linear System Of Equation. by Nzabonimpa, Godfrey

“…It is found out that Gaussian elimination is an algorithm in linear algebra for solving a system of linear equations and can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix Whereas Cho!…”
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Coarse-Grained Column Agglomeration Parallel Algorithm for LU Factorization Using Multi-Threaded MATLAB by Osama Sabir, Reza Alebrahim

“…MATLAB programing language is one of the most popular scientific computing tools, especially for solving linear algebra problems. LU factorization is an essential component for the direct solution of linear equations systems. …”
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The Principle of Mathematical Induction: Applications in Physical Optics by Joseph Ivin Thomas

“…In the contemporary university milieu, the demonstrative scheme is taught as part of a course in discrete mathematics, set theory, number theory, graph theory, group theory, game theory, linear algebra, logic, and combinatorics. In theoretical computer science, it bears the pivotal role of developing the appropriate cognitive skills necessary for the effective design and implementation of algorithms, assessing for both their correctness and complexity. …”
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Split-and-Combine Singular Value Decomposition for Large-Scale Matrix by Jengnan Tzeng

“…The singular value decomposition (SVD) is a fundamental matrix decomposition in linear algebra. It is widely applied in many modern techniques, for example, high- dimensional data visualization, dimension reduction, data mining, latent semantic analysis, and so forth. …”
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Calculation of ecological land-footprint - based on the input-output model and focusing on the imported commodities by Imre Dobos, Brigitta Tóth-Bozó

“…In addition, we allocate the latter again among final consumption and exports using the framework of linear algebra and matrix arithmetic. We also propose ways of extending the model to overcome the general but misleading assumption in the literature that imported commodities have an equal per unit ecological footprint to domestic products, an approach that is based on the idea that trading partners have the same technological background.…”
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A Comparison of Gaussian Elimination and Cholesky Decomposition Methods in Solving a System of Linear Equations. by Niringiye, Richard

“…It is found out that Gaussian elimination is an algorithm in linear algebra for solving a system of linear equations and can also be used to find the rank of a matrix, to calculate the determinant of a matrix, and to calculate the inverse of an invertible square matrix Whereas Cholesky decomposition is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions.…”
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Proximal Alternating Direction Method with Relaxed Proximal Parameters for the Least Squares Covariance Adjustment Problem by Minghua Xu, Yong Zhang, Qinglong Huang, Zhenhua Yang

“…This problem may arise in several areas of numerical linear algebra or come from finance industry or statistics and thus has many applications. …”
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Exploring parameter dependence of atomic minima with implicit differentiation by Ivan Maliyov, Petr Grigorev, Thomas D. Swinburne

“…Here, the implicit derivative of functions defined as a fixed point is used to Taylor-expand the energy and structure of atomic minima in potential parameters, evaluating terms via automatic differentiation, dense linear algebra or a sparse operator approach. The latter allows efficient forward and backpropagation through relaxed structures of arbitrarily large systems. …”
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Computation of Graph Fourier Transform Centrality Using Graph Filter by Chien-Cheng Tseng, Su-Ling Lee

“…To reduce the computational complexity of GFTC, a linear algebra method based on Frobenius norm of error matrix is applied to convert the spectral-domain GFTC computation task to vertex-domain one such that GFTC can be computed by using polynomial graph filtering method. …”
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