相关论文: Two-Stage Block Orthogonalization to Improve Perfo…

We integrate random sketching techniques into block orthogonalization schemes needed for s-step GMRES. The resulting block orthogonalization schemes generate the basis vectors whose overall orthogonality error is bounded by machine…

Communication, i.e., data movement, is a critical bottleneck for the performance of classical Krylov subspace method solvers on modern computer architectures. Variants of these methods which avoid communication have been introduced, which,…

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…

Krylov methods provide a fast and highly parallel numerical tool for the iterative solution of many large-scale sparse linear systems. To a large extent, the performance of practical realizations of these methods is constrained by the…

Krylov subspace methods are an essential building block in numerical simulation software. The efficient utilization of modern hardware is a challenging problem in the development of these methods. In this work, we develop Krylov subspace…

Two-stage orthogonalization is essential in numerical algorithms such as Krylov subspace methods. For this task we need to orthogonalize a matrix $A$ against another matrix $V$ with orthonormal columns. A common approach is to employ the…

The GMRES method is used to solve sparse, non-symmetric systems of linear equations arising from many scientific applications. The solver performance within a single node is memory bound, due to the low arithmetic intensity of its…

3D intelligence leverages rich 3D features and stands as a promising frontier in AI, with 3D rendering fundamental to many downstream applications. 3D Gaussian Splatting (3DGS), an emerging high-quality 3D rendering method, requires…

Gauss-Seidel (GS) relaxation is often employed as a preconditioner for a Krylov solver or as a smoother for Algebraic Multigrid (AMG). However, the requisite sparse triangular solve is difficult to parallelize on many-core architectures…

Communication-avoiding and pipelined variants of Krylov solvers are critical for the scalability of linear system solvers on future exascale architectures. We present low synchronization variants of iterated classical (CGS) and modified…

Primal and dual block coordinate descent methods are iterative methods for solving regularized and unregularized optimization problems. Distributed-memory parallel implementations of these methods have become popular in analyzing large…

The block classical Gram--Schmidt (BCGS) algorithm and its reorthogonalized variant are widely-used methods for computing the economic QR factorization of block columns $X$ due to their lower communication cost compared to other approaches…

3D Gaussian Splatting (3DGS) has established itself as an efficient representation for real-time, high-fidelity 3D scene reconstruction. However, scaling 3DGS to large and unbounded scenes such as city blocks remains difficult. Existing…

In a general graph data structure like an adjacency matrix, when edges are homogeneous, the connectivity of two nodes can be sufficiently represented using a single bit. This insight has, however, not yet been adequately exploited by the…

Reconfigurable intelligent surfaces (RISs) are often assumed to allow continuous phase control over all elements, leading to hardware cost that scales with the number of elements. Treating the phase of each element as a discrete variable is…

The Orthomin ( Omin ) and the Generalized Minimal Residual method ( GMRES ) are commonly used iterative methods for approximating the solution of non-symmetric linear systems. The s-step generalizations of these methods enhance their data…

The solution of eigenproblems is often a key computational bottleneck that limits the tractable system size of numerical algorithms, among them electronic structure theory in chemistry and in condensed matter physics. Large eigenproblems…

Block-tridiagonal systems are prevalent in state estimation and optimal control, and solving these systems is often the computational bottleneck. Improving the underlying solvers therefore has a direct impact on the real-time performance of…

Recent works demonstrate the advantages of hardware rasterization for 3D Gaussian Splatting (3DGS) in forward-pass rendering through fast GPU-optimized graphics and fixed memory footprint. However, extending these benefits to backward-pass…

Stochastic Optimization is a cornerstone of operations research, providing a framework to solve optimization problems under uncertainty. Despite the development of numerous algorithms to tackle these problems, several persistent challenges…