Applying approximate LU-factorizations as preconditioners in eight iterative methods for solving systems of linear algebraic equations [PDF]
Open Mathematics, 2013 AbstractMany problems arising in different fields of science and engineering can be reduced, by applying some appropriate discretization, either to a system of linear algebraic equations or to a sequence of such systems. The solution of a system of linear algebraic equations is very often the most time-consuming part of the computational process during
Zlatev Zahari, Georgiev Krassimir
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Performance impact of precision reduction in sparse linear systems solvers. [PDF]
PeerJ Comput Sci, 2022 It is well established that reduced precision arithmetic can be exploited to accelerate the solution of dense linear systems. Typical examples are mixed precision algorithms that reduce the execution time and the energy consumption of parallel solvers ...
Zounon M, Higham NJ, Lucas C, Tisseur F.
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Pseudoinverse preconditioners and iterative methods for large dense linear least-squares problems [PDF]
Bulletin of Computational Applied Mathematics, 2013 We address the issue of approximating the pseudoinverse of the coefficient matrix for dynamically building preconditioning strategies for the numerical solution of large dense linear least-squares problems.
Oskar Cahueñas +2 more
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AIMS Mathematics, 2023 We consider the preconditioned iterative methods for the linear systems arising from the finite volume discretization of spatial balanced fractional diffusion equations where the fractional differential operators are comprised of both Riemann-Liouville ...
Xiaofeng Guo, Jianyu Pan
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A Class of Iterative Solvers for the Helmholtz Equation: Factorizations, Sweeping Preconditioners, Source Transfer, Single Layer Potentials, Polarized Traces, and Optimized Schwarz Methods [PDF]
SIAM Review, 2016 Solving time-harmonic wave propagation problems by iterative methods is a difficult task, and over the last two decades, an important research effort has gone into developing preconditioners for the simplest representative of such wave propagation ...
M. Gander, Hui Zhang
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Rational Approximations in Robust Preconditioning of Multiphysics Problems
Mathematics, 2022 Multiphysics or multiscale problems naturally involve coupling at interfaces which are manifolds of lower dimensions. The block-diagonal preconditioning of the related saddle-point systems is among the most efficient approaches for numerically solving ...
Stanislav Harizanov +2 more
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Pragmatic solvers for 3D Stokes and elasticity problems with heterogeneous coefficients: evaluating modern incomplete LDLT preconditioners [PDF]
Solid Earth, 2020 The need to solve large saddle point systems within computational Earth sciences is ubiquitous. Physical processes giving rise to these systems include porous flow (the Darcy equations), poroelasticity, elastostatics, and highly viscous flows (the Stokes
P. Sanan +3 more
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The effect of near-zone preconditioning on electromagnetic integral equations of first and second kind [PDF]
Advances in Radio Science, 2013 The linear equation systems which arise from the discretization of surface integral equations are conveniently solved with iterative methods because of the possibility to employ fast integral methods like the Multilevel Fast Multipole Method.
O. Wiedenmann, T. F. Eibert
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Reusing Preconditioners in Projection Based Model Order Reduction Algorithms
IEEE Access, 2020 Dynamical systems are pervasive in almost all engineering and scientific applications. Simulating such systems is computationally very intensive. Hence, Model Order Reduction (MOR) is used to reduce them to a lower dimension.
Navneet Pratap Singh, Kapil Ahuja
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Preconditioners for Krylov subspace methods: An overview
GAMM-Mitteilungen, 2020 When simulating a mechanism from science or engineering, or an industrial process, one is frequently required to construct a mathematical model, and then resolve this model numerically. If accurate numerical solutions are necessary or desirable, this can
J. Pearson, J. Pestana
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