Related papers: An Integer Arithmetic-Based Sparse Linear Solver U…
We consider linear sparse recovery problems where additional structure regarding the support of the solution is known. The form of the structure considered is non-overlapping sets of indices that each contain part of the support. An…
This paper presents the sparsifying preconditioner for the time-harmonic Maxwell's equations in the integral formulation. Following the work on sparsifying preconditioner for the Lippmann-Schwinger equation, this paper generalizes that…
Parametric radiative transfer equation (RTE) occurs in multi-query applications such as uncertainty quantification, inverse problems, and sensitivity analysis, which require solving RTE multiple times for a range of parameters.…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
A robust multilevel preconditioner based on the hybridizable discontinuous Galerkin method for the Helmholtz equation with high wave number is presented in this paper. There are two keys in our algorithm, one is how to choose a suitable…
By incorporating a new matrix splitting and the momentum acceleration into the relaxed-based matrix splitting (RMS) method \cite{soso2023}, a generalization of the RMS (GRMS) iterative method for solving the generalized absolute value…
We present GFORS, a GPU-accelerated framework for large binary integer programs. It couples a first-order (PDHG-style) routine that guides the search in the continuous relaxation with a randomized, feasibility-aware sampling module that…
The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric…
Solving sparse linear systems lies at the core of numerous computational applications. Consequently, understanding the performance of recently proposed alternatives to the established IEEE 754 floating-point numbers, such as bfloat16 and…
Recent development on mixed precision techniques has largely enhanced the performance of various linear algebra solvers, one of which being the solver for the least squares problem $\min_{x}\lVert b-Ax\rVert_{2}$. By transforming least…
We examine the use of a two-level deflation preconditioner combined with GMRES to locally solve the subdomain systems arising from applying domain decomposition methods to Helmholtz problems. Our results show that the direct solution method…
This paper presents an efficient Krylov subspace iterative solver for the three-dimensional (3D) Helmholtz equation with non-constant coefficients and absorbing boundary conditions, combining high-resolution compact schemes with low-order…
We study the general integer programming problem where the number of variables $n$ is a variable part of the input. We consider two natural parameters of the constraint matrix $A$: its numeric measure $a$ and its sparsity measure $d$. We…
When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…
Brown and Walker (1997) showed that GMRES determines a least squares solution of $ A x = b $ where $ A \in {\bf R}^{n \times n} $ without breakdown for arbitrary $ b, x_0 \in {\bf R}^n $ if and only if $A$ is range-symmetric, i.e. $ {\cal…
Generalized inverses play a fundamental role in numerical linear algebra, particularly when matrices are rectangular, singular, or rank deficient. Even when the input matrix is sparse, generalized inverses such as the M-P pseudoinverse are…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
The performance of finite element solvers on modern computer architectures is typically memory bound for sufficiently large problems. The main cause for this is that loading matrix elements from RAM into CPU cache is significantly slower…
Scalable Gaussian process (GP) inference is essential for sequential decision-making tasks, yet improving GP scalability remains a challenging problem with many open avenues of research. This paper focuses on iterative GPs, where iterative…
Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…