Related papers: Block variants of the COCG and COCR methods for so…
This paper deals with the definition and optimization of augmentation spaces for faster convergence of the conjugate gradient method in the resolution of sequences of linear systems. Using advanced convergence results from the literature,…
By reducing the number of global synchronization bottlenecks per iteration and hiding communication behind useful computational work, pipelined Krylov subspace methods achieve significantly improved parallel scalability on present-day HPC…
We study Kaczmarz type methods to solve consistent linear matrix equations. We first present a block Kaczmarz (BK) method that employs a deterministic cyclic row selection strategy. Assuming that the associated coefficient matrix has full…
We study the use of Krylov subspace recycling for the solution of a sequence of slowly-changing families of linear systems, where each family consists of shifted linear systems that differ in the coefficient matrix only by multiples of the…
This work presents a new Krylov-subspace-recycling method for efficiently solving sequences of linear systems of equations characterized by varying right-hand sides and symmetric-positive-definite matrices. As opposed to typical truncation…
In this paper a new block-structure method is presented for the solution of the well-known from gravity theory matrix system of equations g{ij}g{jk}=delta{i}{k} (with respect to the unknown covariant components g{ij} and by known…
In this paper, by regarding the two-subspace Kaczmarz method [20] as an alternated inertial randomized Kaczmarz algorithm we present a new convergence rate estimate which is shown to be better than that in [20] under a mild condition.…
We review our recently developed electronic structure calculation methods used for the dynamics of large-scale solids or liquids with an efficient algorithm for large scale simultaneous linear equations. The electronic structure calculation…
The dominant cost of most lattice QCD simulations is the inversion of the Dirac operator required to calculate the force term in the RHMC update. One way to improve this situation is to use multiple pseudofermions, which reduces the size…
Saddle point problems arise in many important practical applications. In this paper we propose and analyze some algorithms for solving symmetric saddle point problems which are based upon the block Gram-Schmidt method. In particular, we…
Motivated by high-dimensional nonlinear optimization problems as well as ill-posed optimization problems arising in image processing, we consider a bilevel optimization model where we seek among the optimal solutions of the inner level…
For a symmetric positive semidefinite linear system of equations $\mathcal{Q} {\bf x} = {\bf b}$, where ${\bf x} = (x_1,\ldots,x_s)$ is partitioned into $s$ blocks, with $s \geq 2$, we show that each cycle of the classical block symmetric…
This work focuses on the development of efficient solvers for the pseudo-stress formulation of the unsteady Stokes problem, discretised by means of a discontinuous Galerkin method on polytopal grids (PolyDG). The introduction of the…
Every numerical general relativistic investigation starts from the solution of the initial value equations at a given time. Astrophysically relevant initial values for different systems lead to distinct set of equations that obey specific…
This paper introduces a nonlinear conjugate gradient method (NCGM) for addressing the robust counterpart of uncertain multiobjective optimization problems (UMOPs). Here, the robust counterpart is defined as the minimum across objective-wise…
This paper deals with maximum entropy completion of partially specified block-circulant matrices. Since positive definite symmetric circulants happen to be covariance matrices of stationary periodic processes, in particular of stationary…
In this article, we propose an accuracy-assuring technique for finding a solution for unsymmetric linear systems. Such problems are related to different areas such as image processing, computer vision, and computational fluid dynamics.…
In this paper we develop randomized Krylov subspace methods for efficiently computing regularized solutions to large-scale linear inverse problems. Building on the recently developed randomized Gram-Schmidt process, where sketched inner…
Nonsmooth composite optimization with orthogonality constraints has a wide range of applications in statistical learning and data science. However, this problem is challenging due to its nonsmooth objective and computationally expensive…
This work presents a quantum algorithm for solving linear systems of equations of the form $\mathbf{A}{\frac{\mathbf{\partial f}}{\mathbf{\partial x}}} = \mathbf{B}\mathbf{f}$, based on the Quantum Singular Value Transformation (QSVT). The…