A Novel Neural Network-Based Approach Comparable to High-Precision Finite Difference Methods by Fanghua Pei, Fujun Cao, Yongbin Ge

“…These basis functions are then used to create trial solutions, which are optimized using the least-squares method to solve for coefficients in a system of linear equations. This method integrates the strengths of streaming PINNs and the traditional least-squares method, offering both flexibility and a high accuracy. …”
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Numerical study of bioheat transfer in a vascular bed with counter-flow mechanisms by K.R. Sreegowrav, R. Indira, Sushma M. Puranik, S. Jagadeesha, S.J. Vishwanatha, K. Ganesh Kumar

“…The resulting system of linear equations provides insights into the thermal dynamics within the vascular bed, with findings represented graphically.…”
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Advantages of Logarithmic Signatures in the Implementation of Crypto Primitives by Yevhen Kotukh, Hennadii Khalimov

“…This leads to an incomplete system of linear equations concerning unknowns and the impossibility of solving them in polynomial time. …”
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Bicubic ribbon surface by V. A. Korotkiy, E. A. Usmanova

“…The proposed approach makes it possible to reduce the size of the characteristic matrix of a system of linear equations with respect to the coefficients included in the equations of bicubic portions. …”
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A QP-Free Algorithm for Finite Minimax Problems by Daolan Han, Jinbao Jian, Qinfeng Zhang

“…Due to the expensive computation for solving QP subproblems with inequality constraints of SQP algorithms, in this paper, a QP-free algorithm which is also called sequential systems of linear equations algorithm is presented. At each iteration, only two systems of linear equations with the same coefficient matrix need to be solved, and the dimension of each subproblem is not of full dimension. …”
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More on Generalizations and Modifications of Iterative Methods for Solving Large Sparse Indefinite Linear Systems by Jen-Yuan Chen, David R. Kincaid, Yu-Chien Li

“…Continuing from the works of Li et al. (2014), Li (2007), and Kincaid et al. (2000), we present more generalizations and modifications of iterative methods for solving large sparse symmetric and nonsymmetric indefinite systems of linear equations. We discuss a variety of iterative methods such as GMRES, MGMRES, MINRES, LQ-MINRES, QR MINRES, MMINRES, MGRES, and others.…”
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Approximate Solution of LR Fuzzy Sylvester Matrix Equations by Xiaobin Guo, Dequan Shang

“…Then we extend the fuzzy linear system into two systems of linear equations according to the arithmetic operations of LR fuzzy numbers. …”
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Cryptanalysis of Loiss Stream Cipher-Revisited by Lin Ding, Chenhui Jin, Jie Guan, Qiuyan Wang

“…In this paper, based on solving systems of linear equations, we propose an improved Guess and Determine attack on Loiss with a time complexity of 2231 and a data complexity of 268, which reduces the time complexity of the Guess and Determine attack proposed by the designers by a factor of 216. …”
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Measuring. Monitoring. Management. Control by B.V. Chuvykin, I.A. Dolgova, G.V. Milovzorov

“…When applying these methods, the restoration of the distorted amplitude of pulsed information signals depending on the frequency-time properties of the signals is carried out at the stage of digital processing of the measuring signal by solving systems of linear equations. Results. Necessary and sufficient conditions for recovery of extreme values of amplitudes of pulse signals are considered, using measuring information of undistorted part of signal and a priori information on its frequency-time properties. …”

A High Efficiency Discontinuous Galerkin Method for 3D Ground-Penetrating Radar Simulation by Shuyang Xue, Changchun Yin, Jing Li, Jiao Zhu, Wuyang Liu

“…This method uses numerical fluxes to ensure the continuity between elements, allowing Maxwell’s equations to be solved within each element without the need to assemble a global matrix or solve large systems of linear equations. As a result, memory consumption can be significantly reduced, and parallel solvers can be applied at the element level, facilitating the construction of high-order schemes to enhance computational accuracy. …”
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Trading off 1-norm and sparsity against rank for linear models using mathematical optimization: 1-norm minimizing partially reflexive ah-symmetric generalized inverses by Fampa, Marcia, Lee, Jon, Ponte, Gabriel

“…The M-P (Moore–Penrose) pseudoinverse has as a key application the computation of least-squares solutions of inconsistent systems of linear equations. Irrespective of whether a given input matrix is sparse, its M-P pseudoinverse can be dense, potentially leading to high computational burden, especially when we are dealing with high-dimensional matrices. …”
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