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We study an auto-calibration problem in which a transform-sparse signal is acquired via compressive sensing by multiple sensors in parallel, but with unknown calibration parameters of the sensors. This inverse problem has an important…
We propose a verified computation method for eigenvalues in a region and the corresponding eigenvectors of generalized Hermitian eigenvalue problems. The proposed method uses complex moments to extract the eigencomponents of interest from a…
The adoption of hybrid GPU-CPU nodes in traditional supercomputing platforms opens acceleration opportunities for electronic structure calculations in materials science and chemistry applications, where medium sized Hermitian generalized…
We consider the problem of mixed linear regression (MLR), where each observed sample belongs to one of $K$ unknown linear models. In practical applications, the proportions of the $K$ components are often imbalanced. Unfortunately, most MLR…
The FEAST algorithm is a subspace iteration method that uses a spectral projector as a rational filter in order to efficiently solve interior eigenvalue problems in parallel. Although the solutions from the FEAST algorithm converge rapidly…
Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…
We study the Maximum Independent Set of Rectangles (MISR) problem, where we are given a set of axis-parallel rectangles in the plane and the goal is to select a subset of non-overlapping rectangles of maximum cardinality. In a recent…
The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
Meshless methods are commonly used to determine numerical solutions to partial differential equations (PDEs) for problems involving free surfaces and/or complex geometries, approximating spatial derivatives at collocation points via local…
Large-scale optimization problems that seek sparse solutions have become ubiquitous. They are routinely solved with various specialized first-order methods. Although such methods are often fast, they usually struggle with not-so-well…
In this paper two types of multgrid methods, i.e., the Rayleigh quotient iteration and the inverse iteration with fixed shift, are developed for solving the Maxwell eigenvalue problem with discontinuous relative magnetic permeability and…
Symmetric linear solves are fundamental to a wide range of scientific and engineering applications, from climate modeling and structural analysis to machine learning and optimization. These workloads often rely on Cholesky (POTRF)…
Parallel implementation of numerical adaptive mesh refinement (AMR)strategies for solving 3D elastostatic contact mechanics problems is an essential step toward complex simulations that exceed current performance levels. This paper…
The eigenvalue problem is a fundamental problem in scientific computing. In this paper, we first give the error analysis for a single step or sweep of Jacobi's method in floating point arithmetic. Then we propose a mixed precision…
In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…
The randomized row method is a popular representative of the iterative algorithm because of its efficiency in solving the overdetermined and consistent systems of linear equations. In this paper, we present an extended randomized multiple…
This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal…
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 introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…