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PyLops—A linear-operator Python library for scalable algebra and optimization
SoftwareX, 2020 Linear operators and optimization are at the core of many algorithms used in signal and image processing, remote sensing, and inverse problems. For small to medium-scale problems, existing software packages (e.g., MATLAB, Python NumPy and SciPy) allow to
Matteo Ravasi, Ivan Vasconcelos
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Computational methods for large-scale inverse problems: a survey on hybrid projection methods [PDF]
SIAM Review, 2021 This paper surveys an important class of methods that combine iterative projection methods and variational regularization methods for large-scale inverse problems.
Julianne Chung, S. Gazzola
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Innovation and Practice of the Linear Algebra Teaching Based on “the Unity of Knowledge and Action”
Frontiers in Educational Research, 2023 : As the fruit of human thought and wisdom, the education law of “the unity of knowledge and action” is an intrinsic requirement for the harmonious and comprehensive development of the human body and mind.
Xiu-li Li +3 more
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Behavioral Sciences, 2022 Computer-based testing is an emerging method to evaluate students’ mathematics learning outcomes. However, algebra problems impose a high cognitive load due to requiring multiple calculation steps, which might reduce students’ performance in computer ...
Jing-Fong Wang +2 more
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Parallel multigrid method for solving inverse problems
MethodsX, 2022 We considered in this work the linear operator equation and used the Landweber iterative method as an iterative solver. After that, we used the multigrid method as an optimization method for obtaining an approximation solution with a highly accurate and ...
H.K. Al-Mahdawi +5 more
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Symbolic Computation Applied to Cauchy Type Singular Integrals
Mathematical and Computational Applications, 2021 The development of operator theory is stimulated by the need to solve problems emerging from several fields in mathematics and physics. At the present time, this theory has wide applications in the study of non-linear differential equations, in linear ...
Ana C. Conceição, Jéssica C. Pires
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On Matrices with Only One Non-SDD Row
Mathematics, 2023 The class of H-matrices, also known as Generalized Diagonally Dominant (GDD) matrices, plays an important role in many areas of applied linear algebra, as well as in a wide range of applications, such as in dynamical analysis of complex networks that ...
Ksenija Doroslovački +1 more
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The Practicality of Stochastic Optimization in Imaging Inverse Problems [PDF]
IEEE Transactions on Computational Imaging, 2019 In this work we investigate the practicality of stochastic gradient descent and its variants with variance-reduction techniques in imaging inverse problems.
Junqi Tang +3 more
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, 2017 The nonnegative inverse eigenvalue problem (NIEP) asks which lists of $n$ complex numbers (counting multiplicity) occur as the eigenvalues of some $n$-by-$n$ entry-wise nonnegative matrix.
Johnson, Charles R. +3 more
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Interval Linear Algebra and Computational Complexity [PDF]
arXiv.org, 2015 This work connects two mathematical fields – computational complexity and interval linear algebra . It introduces the basic topics of interval linear algebra – regularity and singularity, full column rank, solving a linear system , deciding solvability ...
J. Horáček, M. Hladík, M. Černý
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