A Preconditioned Iterative Method for Solving Systems of Nonlinear Equations Having Unknown Multiplicity [PDF]
Algorithms, 2017 A modification to an existing iterative method for computing zeros with unknown multiplicities of nonlinear equations or a system of nonlinear equations is presented.
Fayyaz Ahmad +6 more
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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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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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Accelerating Cosmic Microwave Background map-making procedure through preconditioning [PDF]
, 2010 Estimation of the sky signal from sequences of time ordered data is one of the key steps in Cosmic Microwave Background (CMB) data analysis, commonly referred to as the map-making problem.
M. Szydlarski +36 more
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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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Nonlinear Preconditioning: How to use a Nonlinear Schwarz Method to Precondition Newton's Method [PDF]
, 2015 For linear problems, domain decomposition methods can be used directly as iterative solvers, but also as preconditioners for Krylov methods. In practice, Krylov acceleration is almost always used, since the Krylov method finds a much better residual ...
Dolean, V. +4 more
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Sparse approximate inverse preconditioners on high performance GPU platforms [PDF]
, 2016 Simulation with models based on partial differential equations often requires the solution of (sequences of) large and sparse algebraic linear systems. In multidimensional domains, preconditioned Krylov iterative solvers are often appropriate for these ...
Bertaccini, Daniele +1 more
core +1 more source