相关论文: A Technical Survey of Sparse Linear Solvers in Ele…

The multi-frontal direct solver is the state-of-the-art algorithm for the direct solution of sparse linear systems. This paper provides computational complexity and memory usage estimates for the application of the multi-frontal direct…

Iterative solutions of sparse linear systems and sparse eigenvalue problems have a fundamental role in vital fields of scientific research and engineering. The crucial computing kernel for such iterative solutions is the multiplication of a…

We present CheSS, the "Chebyshev Sparse Solvers" library, which has been designed to solve typical problems arising in large-scale electronic structure calculations using localized basis sets. The library is based on a flexible and…

Generally, discretization of partial differential equations (PDEs) creates a sequence of linear systems $A_k x_k = b_k, k = 0, 1, 2, ..., N$ with well-known and structured sparsity patterns. Preconditioners are often necessary to achieve…

Sparse autoencoders (SAEs) are a popular method for interpreting concepts represented in large language model (LLM) activations. However, there is a lack of evidence regarding the validity of their interpretations due to the lack of a…

Linear discriminant analysis (LDA) is a classical method for dimensionality reduction, where discriminant vectors are sought to project data to a lower dimensional space for optimal separability of classes. Several recent papers have…

The main objective of this work consists in analyzing sub-structuring method for the parallel solution of sparse linear systems with matrices arising from the discretization of partial differential equations such as finite element, finite…

Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids…

Sparse linear iterative solvers are essential for many large-scale simulations. Much of the runtime of these solvers is often spent in the implicit evaluation of matrix polynomials via a sequence of sparse matrix-vector products. A variety…

Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…

We define the notion of effective stiffness and show that it can used to build sparsifiers, algorithms that sparsify linear systems arising from finite-element discretizations of PDEs. In particular, we show that sampling $O(n\log n)$…

Sparse system identification of nonlinear dynamic systems is still challenging, especially for stiff and high-order differential equations for noisy measurement data. The use of highly correlated functions makes distinguishing between true…

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated…

Our goal is to present an elementary approach to the analysis and programming of sparse grid finite element methods. This family of schemes can compute accurate solutions to partial differential equations, but using far fewer degrees of…

This article discusses the uncertainty quantification (UQ) for time-independent linear and nonlinear partial differential equation (PDE)-based systems with random model parameters carried out using sampling-free intrusive stochastic…

Representation learning has become an effective technique utilized by electronic design automation (EDA) algorithms, which leverage the natural representation of workflow elements as images, grids, and graphs. By addressing challenges…

Efficient and suitably preconditioned iterative solvers for elliptic partial differential equations (PDEs) of the convection-diffusion type are used in all fields of science and engineering. To achieve optimal performance, solvers have to…

Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…

We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…

Incomplete factorizations have long been popular general-purpose algebraic preconditioners for solving large sparse linear systems of equations. Guaranteeing the factorization is breakdown free while computing a high quality preconditioner…