Related papers: General framework for re-assuring numerical reliab…
An efficient Krylov subspace algorithm for computing actions of the $\varphi$ matrix function for large matrices is proposed. This matrix function is widely used in exponential time integration, Markov chains and network analysis and many…
Krylov subspace methods are considered a standard tool to solve large systems of linear algebraic equations in many scientific disciplines such as image restoration or solving partial differential equations in mechanics of continuum. In the…
The paper discusses the efficiency of the classical BiCGStab method and several of its modifications for solving systems with multiple right-hand side vectors. These iterative methods are widely used for solving systems with large sparse…
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…
This paper derives a new class of adaptive regularization parameter choice strategies that can be effectively and efficiently applied when regularizing large-scale linear inverse problems by combining standard Tikhonov regularization and…
Many Krylov subspace methods for shifted linear systems take advantage of the invariance of the Krylov subspace under a shift of the matrix. However, exploiting this fact in the non-Hermitian case introduces restrictions; e.g., initial…
Multigrid methods have been a popular approach for solving linear systems arising from the discretization of partial differential equations (PDEs) for several decades. They are particularly effective for accelerating convergence rates with…
We present a new short-recurrence reaidual-optimal Krylov subspace recycling method for sequences of Hermitian systems of linear equations with a fixed system matrix and changing right-hand sides. Such sequences of linear systems occur…
For several classes of mathematical models that yield linear systems, the splitting of the matrix into its Hermitian and skew Hermitian parts is naturally related to properties of the underlying model. This is particularly so for…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…
The parallel linear equations solver capable of effectively using 1000+ processors becomes the bottleneck of large-scale implicit engineering simulations. In this paper, we present a new hierarchical parallel master-slave-structural…
Quantum Krylov algorithms have emerged as a promising approach for ground-state energy estimation in the near-term quantum computing era. A major challenge, however, lies in their inherently substantial sampling cost, primarily due to the…
This paper presents our work on designing a parallel platform for large-scale reservoir simulations. Detailed components, such as grid and linear solver, and data structures are introduced, which can serve as a guide to parallel reservoir…
Pipeline Parallelism (PP) enables large neural network training on small, interconnected devices by splitting the model into multiple stages. To maximize pipeline utilization, asynchronous optimization is appealing as it offers 100%…
A wide range of applications necessitates solving large-scale ill-posed problems contaminated by noise. Krylov subspace regularization methods are particularly advantageous in this context, as they rely solely on matrix-vector…
A Krylov subspace recycling method for the efficient evaluation of a sequence of matrix functions acting on a set of vectors is developed. The method improves over the recycling methods presented in [Burke et al., arXiv:2209.14163, 2022] in…
Many practical imaging systems suffer from uncertainty in acquisition geometry -- such as projection angles in computed tomography or sensor positions in photoacoustic tomography -- leading to nonlinear inverse problems that require joint…
Sparse matrices have recently played a significant and impactful role in scientific computing, including artificial intelligence-related fields. According to historical studies on sparse matrix--vector multiplication (SpMV), Krylov subspace…
The Preconditioned Conjugate Gradient method is often employed for the solution of linear systems of equations arising in numerical simulations of physical phenomena. While being widely used, the solver is also known for its lack of…
Constrained least squares problems arise in a variety of applications, and many iterative methods are already available to compute their solutions. This paper proposes a new efficient approach to solve nonnegative linear least squares…