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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Math-Phys-Chem Approaches to Life by Hitomi Kitaojima, Shigeru Kanemitsu

“…They correspond to three mathematical dsciplines—probability, linear algebra and free groups, respectively. We shall give some basics for the Rényi (𝛼)-entropy, Chebyshev polynomials and the notion of free groups inrespective places. …”
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Transfer functions of a time-varying control system by Volt Avdieiev

“…This makes it possible to transform differential equations into algebraic ones, as a result to use the developed apparatus of linear algebra to solve problems of analysis and synthesis. …”
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Extensions of Riordan Arrays and Their Applications by Paul Barry

“…The methods used include generating functions, linear algebra, weighted compositions, and linear recurrences. …”
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The Discriminative Lexicon: A Unified Computational Model for the Lexicon and Lexical Processing in Comprehension and Production Grounded Not in (De)Composition but in Linear Discr... by R. Harald Baayen, Yu-Ying Chuang, Elnaz Shafaei-Bajestan, James P. Blevins

“…This novel theory is inspired by word and paradigm morphology but operationalizes the concept of proportional analogy using the mathematics of linear algebra. It embraces the discriminative perspective on language, rejecting the idea that words’ meanings are compositional in the sense of Frege and Russell and arguing instead that the relation between form and meaning is fundamentally discriminative. …”
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Elastodynamic modeling and analysis of a 4SRRR overconstrained parallel robot by B. Wang, Y. Zhao, C. Yang, X. Hu, Y. Zhao

“…Second, based on the theory of multipoint constraint elements and linear algebra, a set of independent displacement coordinates is established for the connection points between rods and the moving platform, rods and rods, and rods and the fixed platform. …”
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Sensitivity and identifiability analysis of COVID-19 pandemic models by O. I. Krivorotko, S. I. Kabanikhin, M. I. Sosnovskaya, D. V. Andornaya

“…The algorithm is built on the sensitivity matrix analysis using the methods of differential and linear algebra. It allows one to determine the parameters that are the least and most sensitive to data changes to build a regularization for solving an identif ication problem of the most accurate pandemic spread scenarios in the region. …”
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Numerical Approach Based on Two-Dimensional Fractional-Order Legendre Functions for Solving Fractional Differential Equations by Qingxue Huang, Fuqiang Zhao, Jiaquan Xie, Lifeng Ma, Jianmei Wang, Yugui Li

“…Then the matrix with the Tau method is utilized to transform this problem into a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. …”
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Laguerre Collocation Method for Solving Fredholm Integro-Differential Equations with Functional Arguments by Burcu Gürbüz, Mehmet Sezer, Coşkun Güler

“…This method transforms the considered problem to a matrix equation which corresponds to a system of linear algebraic equations. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments. …”
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Some Upper Matrix Bounds for the Solution of the Continuous Algebraic Riccati Matrix Equation by Zübeyde Ulukök, Ramazan Türkmen

“…We propose diverse upper bounds for the solution matrix of the continuous algebraic Riccati matrix equation (CARE) by building the equivalent form of the CARE and using some matrix inequalities and linear algebraic techniques. Finally, numerical example is given to demonstrate the effectiveness of the obtained results in this work as compared with some existing results in the literature. …”
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