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Sparse linear systems are typically solved using preconditioned iterative methods, but applying preconditioners via sparse triangular solves introduces bottlenecks due to irregular memory accesses and data dependencies. This work leverages…
Sparse tensor computing is a core computational part of numerous applications in areas such as data science, graph processing, and scientific computing. Sparse tensors offer the potential of skipping unnecessary computations caused by zero…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
Sparse-dense linear algebra is crucial in many domains, but challenging to handle efficiently on CPUs, GPUs, and accelerators alike; multiplications with sparse formats like CSR and CSF require indirect memory lookups. In this work, we…
Sparse matrix-vector multiplication (SpMxV) is a kernel operation widely used in iterative linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers. Matrices with irregular sparsity patterns make it…
Nowadays, several industrial applications are being ported to parallel architectures. In fact, these platforms allow acquire more performance for system modelling and simulation. In the electric machines area, there are many problems which…
This paper discusses parGeMSLR, a C++/MPI software library for the solution of sparse systems of linear algebraic equations via preconditioned Krylov subspace methods in distributed-memory computing environments. The preconditioner…
We present a fast sparse matrix permutation algorithm tailored to linear systems arising from triangle meshes. Our approach produces nested-dissection-style permutations while significantly reducing permutation runtime overhead. Rather than…
Real-time trajectory optimization for nonlinear constrained autonomous systems is critical and typically performed by CPU-based sequential solvers. Specifically, reliance on global sparse linear algebra or the serial nature of dynamic…
Iterative methods for solving large sparse systems of linear equations are widely used in many HPC applications. Extreme scaling of these methods can be difficult, however, since global communication to form dot products is typically…
As integrated circuits become increasingly complex, the demand for efficient and accurate simulation solvers continues to rise. Traditional solvers often struggle with large-scale sparse systems, leading to prolonged simulation times and…
We develop and analyze new scheduling algorithms for solving sparse triangular linear systems (SpTRSV) in parallel. Our approach produces highly efficient synchronous schedules for the forward- and backward-substitution algorithm. Compared…
Exact recovery of a sparse solution for an underdetermined system of linear equations implies full search among all possible subsets of the dictionary, which is computationally intractable, while l1 minimization will do the job when a…
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…
Sparse Matrix-Matrix multiplication is a key kernel that has applications in several domains such as scientific computing and graph analysis. Several algorithms have been studied in the past for this foundational kernel. In this paper, we…
The sparse matrix-vector multiplication (SpMxV) is a kernel operation widely used in iterative linear solvers. The same sparse matrix is multiplied by a dense vector repeatedly in these solvers. Matrices with irregular sparsity patterns…
Linear system solving is a key tool for computational power system studies, e.g., optimal power flow, transmission switching, or unit commitment. CPU-based linear system solver speeds, however, have saturated in recent years. Emerging…
We consider the problem of developing an efficient multi-threaded implementation of the matrix-vector multiplication algorithm for sparse matrices with structural symmetry. Matrices are stored using the compressed sparse row-column format…
Supercomputers are equipped with an increasingly large number of cores to use computational power as a way of solving problems that are otherwise intractable. Unfortunately, getting serial algorithms to run in parallel to take advantage of…
Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods…