Related papers: Matrix Equations, Sparse Solvers: M-M.E.S.S.-2.0.1…
This Ph.D. thesis contains original contributions to several areas within the disciplines of disordered systems, numerical linear algebra, and scientific computing: (1) Theoretical and numerical study of the errors caused by using certain…
Solving sparse linear systems from discretized PDEs is challenging. Direct solvers have in many cases quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and…
Matrix computations are a fundamental building-block of edge computing systems, with a major recent uptick in demand due to their use in AI/ML training and inference procedures. Existing approaches for distributing matrix computations…
In machine learning and data mining, linear models have been widely used to model the response as parametric linear functions of the predictors. To relax such stringent assumptions made by parametric linear models, additive models consider…
Scaling problems have a rich and diverse history, and thereby have found numerous applications in several fields of science and engineering. For instance, the matrix scaling problem has had applications ranging from theoretical computer…
Recent technological advancements have led to the rapid generation of high-throughput biological data, which can be used to address novel scientific questions in broad areas of research. These data can be thought of as a large matrix with…
This work investigates an efficient solution to two fundamental problems in topology optimization of frame structures. The first one involves minimizing structural compliance under linear-elastic equilibrium and weight constraint, while the…
Recovery of low-rank matrices has recently seen significant activity in many areas of science and engineering, motivated by recent theoretical results for exact reconstruction guarantees and interesting practical applications. A number of…
We introduce a family of numerical algorithms for the solution of linear system in higher dimensions with the matrix and right hand side given and the solution sought in the tensor train format. The proposed methods are rank--adaptive and…
A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…
In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming…
We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…
The computation of a matrix function $f(A)$ is an important task in scientific computing appearing in machine learning, network analysis and the solution of partial differential equations. In this work, we use only matrix-vector products…
We present an efficient mathematical framework based on the linearly-involved Moreau-enhanced-over-subspace (LiMES) model. Two concrete applications are considered: sparse modeling and robust regression. The popular minimax concave (MC)…
This paper addresses the problem of planning under uncertainty in large Markov Decision Processes (MDPs). Factored MDPs represent a complex state space using state variables and the transition model using a dynamic Bayesian network. This…
State-space models (SSMs) are a common tool for modeling multi-variate discrete-time signals. The linear-Gaussian (LG) SSM is widely applied as it allows for a closed-form solution at inference, if the model parameters are known. However,…
The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In…
Matrix-matrix multiplication is a basic operation in linear algebra and an essential building block for a wide range of algorithms in various scientific fields. Theory and implementation for the dense, square matrix case are well-developed.…
In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…