Related papers: A Nested Krylov Method Using Half-Precision Arithm…
In the present paper, we propose Krylov-based methods for solving large-scale differential Sylvester matrix equations having a low rank constant term. We present two new approaches for solving such differential matrix equations. The first…
Meeting service-level objectives (SLOs) in Large Language Models (LLMs) serving is critical, but managing the high variability in load presents a significant challenge. Recent advancements in FP8 inference, backed by native hardware…
In this paper, we introduce a unified framework for nonlinear Krylov subspace methods (nlKrylov) to solve systems of nonlinear equations. Building on classical GCR-like/type linear Krylov solvers such as GMRESR, we generalize these…
Many scientific applications require the evaluation of the action of the matrix function over a vector and the most common methods for this task are those based on the Krylov subspace. Since the orthogonalization cost and memory requirement…
The solution of sequences of shifted linear systems is a classic problem in numerical linear algebra, and a variety of efficient methods have been proposed over the years. Nevertheless, there still exist challenging scenarios witnessing a…
Inverse problems arise in various scientific and engineering applications, necessitating robust numerical methods for their solution. In this work, we consider the effectiveness of Krylov subspace iterative methods, including GMRES, QMR,…
This paper gives an analysis and an evaluation of linear algebra operations on Graphics Processing Unit (GPU) with complex number arithmetics with double precision. Knowing the performance of these operations, iterative Krylov methods are…
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,…
Efficient simulation of nonlinear and dispersive free-surface flows governed by the incompressible Navier-Stokes equations remains a central challenge in ocean and coastal engineering. The computational bottleneck arises from solving a…
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.…
Modern GPUs are equipped with tensor cores (TCs) that are commonly used for matrix multiplication in artificial intelligence workloads. However, because they have high computational throughput, they can lead to significant performance gains…
Recently, enlarged Krylov subspace methods, that consists of enlarging the Krylov subspace by a maximum of t vectors per iteration based on the domain decomposition of the graph of A, were introduced in the aim of reducing communication…
With the increasing complexity of machine learning models, managing computational resources like memory and processing power has become a critical concern. Mixed precision techniques, which leverage different numerical precisions during…
Iterative Krylov projection methods have become widely used for solving large-scale linear inverse problems. However, methods based on orthogonality include the computation of inner-products, which become costly when the number of…
Analogues of the conjugate gradient method, MINRES, and GMRES are derived for solving boundary value problems (BVPs) involving second-order differential operators. Two challenges arise: imposing the boundary conditions on the solution while…
Nesterov's well-known scheme for accelerating gradient descent in convex optimization problems is adapted to accelerating stationary iterative solvers for linear systems. Compared with classical Krylov subspace acceleration methods, the…
Large-scale numerical simulations often come at the expense of daunting computations. High-Performance Computing has enhanced the process, but adapting legacy codes to leverage parallel GPU computations remains challenging. Meanwhile,…
This work is on a user-friendly reduced basis method for solving a family of parametric PDEs by preconditioned Krylov subspace methods including the conjugate gradient method, generalized minimum residual method, and bi-conjugate gradient…
Krylov subspace methods are extensively used in scientific computing to solve large-scale linear systems. However, the performance of these iterative Krylov solvers on modern supercomputers is limited by expensive communication costs. The…
Methods for solving scientific computing and inference problems, such as kernel- and neural network-based approaches for partial differential equations (PDEs), inverse problems, and supervised learning tasks, depend crucially on the choice…