24,508 research outputs found
Preconditioning complex symmetric linear systems
A new polynomial preconditioner for symmetric complex linear systems based on
Hermitian and skew-Hermitian splitting (HSS) for complex symmetric linear
systems is herein presented. It applies to Conjugate Orthogonal Conjugate
Gradient (COCG) or Conjugate Orthogonal Conjugate Residual (COCR) iterative
solvers and does not require any estimation of the spectrum of the coefficient
matrix. An upper bound of the condition number of the preconditioned linear
system is provided. Moreover, to reduce the computational cost, an inexact
variant based on incomplete Cholesky decomposition or orthogonal polynomials is
proposed. Numerical results show that the present preconditioner and its
inexact variant are efficient and robust solvers for this class of linear
systems. A stability analysis of the method completes the description of the
preconditioner.Comment: 26 pages, 4 figures, 4 table
A Multi-GPU Programming Library for Real-Time Applications
We present MGPU, a C++ programming library targeted at single-node multi-GPU
systems. Such systems combine disproportionate floating point performance with
high data locality and are thus well suited to implement real-time algorithms.
We describe the library design, programming interface and implementation
details in light of this specific problem domain. The core concepts of this
work are a novel kind of container abstraction and MPI-like communication
methods for intra-system communication. We further demonstrate how MGPU is used
as a framework for porting existing GPU libraries to multi-device
architectures. Putting our library to the test, we accelerate an iterative
non-linear image reconstruction algorithm for real-time magnetic resonance
imaging using multiple GPUs. We achieve a speed-up of about 1.7 using 2 GPUs
and reach a final speed-up of 2.1 with 4 GPUs. These promising results lead us
to conclude that multi-GPU systems are a viable solution for real-time MRI
reconstruction as well as signal-processing applications in general.Comment: 15 pages, 10 figure
Over-constrained Weierstrass iteration and the nearest consistent system
We propose a generalization of the Weierstrass iteration for over-constrained
systems of equations and we prove that the proposed method is the Gauss-Newton
iteration to find the nearest system which has at least common roots and
which is obtained via a perturbation of prescribed structure. In the univariate
case we show the connection of our method to the optimization problem
formulated by Karmarkar and Lakshman for the nearest GCD. In the multivariate
case we generalize the expressions of Karmarkar and Lakshman, and give
explicitly several iteration functions to compute the optimum.
The arithmetic complexity of the iterations is detailed
On Relaxed Averaged Alternating Reflections (RAAR) Algorithm for Phase Retrieval from Structured Illuminations
In this paper, as opposed to the random phase masks, the structured
illuminations with a pixel-dependent deterministic phase shift are considered
to derandomize the model setup. The RAAR algorithm is modified to adapt to two
or more diffraction patterns, and the modified RAAR algorithm operates in
Fourier domain rather than space domain. The local convergence of the RAAR
algorithm is proved by some eigenvalue analysis. Numerical simulations is
presented to demonstrate the effectiveness and stability of the algorithm
compared to the HIO (Hybrid Input-Output) method. The numerical performances
show the global convergence of the RAAR in our tests.Comment: 17 pages, 26 figures, submitting to Inverse Problem
Accelerating Wilson Fermion Matrix Inversions by Means of the Stabilized Biconjugate Gradient Algorithm
The stabilized biconjugate gradient algorithm BiCGStab recently presented by
van der Vorst is applied to the inversion of the lattice fermion operator in
the Wilson formulation of lattice Quantum Chromodynamics. Its computational
efficiency is tested in a comparative study against the conjugate gradient and
minimal residual methods. Both for quenched gauge configurations at beta= 6.0
and gauge configurations with dynamical fermions at beta=5.4, we find BiCGStab
to be superior to the other methods. BiCGStab turns out to be particularly
useful in the chiral regime of small quark masses.Comment: 25 pages, WUB 94-1
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