Iterative Methods and Preconditioners for Systems of Linear Equations
, 2022 This book gives an introduction to iterative methods and preconditioning for solving discretized elliptic partial differential equations (PDEs) and optimal control problems governed by elliptic PDEs, for which the use of matrix-free procedures is ...
Ciaramella, Gabriele, Gander, Martin J.
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Performance impact of precision reduction in sparse linear systems solvers [PDF]
PeerJ Computer Science, 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 ...
Mawussi Zounon +3 more
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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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On iterative methods and implicit-factorization preconditioners for regularized saddle-point systems [PDF]
, 2005 We consider conjugate-gradient like methods for solving block symmetric indefinite linear systems that arise from saddle point problems or, in particular, regularizations thereof. Such methods require preconditioners that preserve certain sub-blocks from the original systems but allow considerable flexibility for the remaining blocks.
Dollar, H +3 more
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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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Generalized Structure Preserving Preconditioners for Frame-Based Image Deblurring
Mathematics, 2020 We are interested in fast and stable iterative regularization methods for image deblurring problems with space invariant blur. The associated coefficient matrix has a Block Toeplitz Toeplitz Blocks (BTTB) like structure plus a small rank correction ...
Davide Bianchi, Alessandro Buccini
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