Related papers: Accelerating CS in Parallel Imaging Reconstruction…
In this paper, a parallel overlapping domain decomposition preconditioner is proposed to solve the linear system of equations arising from the extended finite element discretization of elastic crack problems. The algorithm partitions the…
Magnetic Resonance Imaging (MRI) acquisitions require extensive scan times, limiting patient throughput and increasing susceptibility to motion artifacts. Accelerated parallel MRI techniques reduce acquisition time by undersampling k-space…
This paper presents a parallel preconditioning approach based on incomplete LU (ILU) factorizations in the framework of Domain Decomposition (DD) for general sparse linear systems. We focus on distributed memory parallel architectures,…
We present a modified version of the PRESB preconditioner for two-by-two block system of linear equations with the coefficient matrix $$\textbf{A}=\left(\begin{array}{cc} F & -G^* G & F \end{array}\right),$$ where $F\in\mathbb{C}^{n\times…
We investigate iterative methods with randomized preconditioners for solving overdetermined least-squares problems, where the preconditioners are based on a random embedding of the data matrix. We consider two distinct approaches: the…
We propose a two-level iterative scheme for solving general sparse linear systems. The proposed scheme consists of a sparse preconditioner that increases the skew-symmetric part and makes the main diagonal of the coefficient matrix as close…
Sparse linear system solvers are computationally expensive kernels that lie at the heart of numerous applications. This paper proposes a flexible preconditioning framework to substantially reduce the time and energy requirements of this…
We present a fast direct solver for structured linear systems based on multilevel matrix compression. Using the recently developed interpolative decomposition of a low-rank matrix in a recursive manner, we embed an approximation of the…
Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice,…
The convergence of the conjugate gradient method for solving large-scale and sparse linear equation systems depends on the spectral properties of the system matrix, which can be improved by preconditioning. In this paper, we develop a…
We propose a preconditioner that can accelerate the rate of convergence of the Multiple Shooting Shadowing (MSS) method. This recently proposed method can be used to compute derivatives of time-averaged objectives (also known as…
Parallel imaging techniques reduce magnetic resonance imaging (MRI) scan time but image quality degrades as the acceleration factor increases. In clinical practice, conservative acceleration factors are chosen because no mechanism exists to…
A parallel and nested version of a frequency filtering preconditioner is proposed for linear systems corresponding to diffusion equation on a structured grid. The proposed preconditioner is found to be robust with respect to jumps in the…
Dose reduction in computed tomography (CT) is essential for decreasing radiation risk in clinical applications. Iterative reconstruction is one of the most promising ways to compensate for the increased noise due to reduction of photon…
Large-scale dynamic inverse problems are often ill-posed due to model complexity and the high dimensionality of the unknown parameters. Regularization is commonly employed to mitigate ill-posedness by incorporating prior information and…
In this note we exploit polynomial preconditioners for the Conjugate Gradient method to solve large symmetric positive definite linear systems in a parallel environment. We put in connection a specialized Newton method to solve the matrix…
We deal with interval parametric systems of linear equations and the goal is to solve such systems, which basically comes down to finding an enclosure for a parametric solution set. Obviously we want this enclosure to be as tight as…
The main computational cost of algorithms for computing reduced-order models of parametric dynamical systems is in solving sequences of very large and sparse linear systems. We focus on efficiently solving these linear systems, arising…
In this work, we consider the solution of fluid-structure interaction problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary…
Compressed sensing is an imaging paradigm that allows one to invert an underdetermined linear system by imposing the a priori knowledge that the sought after solution is sparse (i.e., mostly zeros). Previous works have shown that if one…