Related papers: A New Matrix Truncation Method for Improving Appro…
Low-Rank Adaptation (LoRA) emerges as a popular parameter-efficient fine-tuning (PEFT) method, which proposes to freeze pretrained model weights and update an additive low-rank trainable matrix. In this work, we study the enhancement of…
A new algorithm to approximate Hermitian matrices by positive semidefinite Hermitian matrices based on modified Cholesky decompositions is presented. In contrast to existing algorithms, this algorithm allows to specify bounds on the…
The low-rank matrix recovery problem often arises in various fields, including signal processing, machine learning, and imaging science. The Riemannian gradient descent (RGD) algorithm has proven to be an efficient algorithm for solving…
We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general, and may refer to a regular sparsity pattern (e.g., block-banded), or be more highly structured (e.g., symmetric…
Randomized methods are becoming increasingly popular in numerical linear algebra. However, few attempts have been made to use them in developing preconditioners. Our interest lies in solving large-scale sparse symmetric positive definite…
Parametric model order reduction by matrix interpolation allows for efficient prediction of the behavior of dynamic systems without requiring knowledge about the underlying parametric dependency. Within this approach, reduced models are…
Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. They usually suffer from the major drawback that the solution is biased towards one of the optimization…
A preconditioning strategy is proposed for the iterative solve of large numbers of linear systems with parameter-dependent matrix and right-hand side which arise during the computation of solution statistics of stochastic elliptic partial…
This paper introduces a novel Transformed Primal-Dual with variable-metric/preconditioner (TPDv) algorithm, designed to efficiently solve affine constrained optimization problems common in nonlinear partial differential equations (PDEs).…
Truncated singular value decomposition (SVD), also known as the best low-rank matrix approximation, has been successfully applied to many domains such as biology, healthcare, and others, where high-dimensional datasets are prevalent. To…
This paper studies a regularized matrix tri-factorization \(A\approx PDQ\), where \(P\) and \(Q\) are side factors and \(D\) is a central core whose conditioning can be explicitly regularized or constrained. The formulation is a structured…
A new polynomial preconditioner for symmetric complex linear systems based on Hermitian and skew-Hermitian splitting (HSS) for complex symmetric linear systems is herein presented. It applies to Conjugate Orthogonal Conjugate Gradient…
The importance of accurate recommender systems has been widely recognized by academia and industry. However, the recommendation quality is still rather low. Recently, a linear sparse and low-rank representation of the user-item matrix has…
Low-rank tensor completion aims to recover a tensor from partially observed entries, and it is widely applicable in fields such as quantum computing and image processing. Due to the significant advantages of the tensor train (TT) format in…
Low-rank tensor approximation techniques attempt to mitigate the overwhelming complexity of linear algebra tasks arising from high-dimensional applications. In this work, we study the low-rank approximability of solutions to linear systems…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
Least squares method is one of the simplest and most popular techniques applied in data fitting, imaging processing and high dimension data analysis. The classic methods like QR and SVD decomposition for solving least squares problems has a…
Preconditioning is a key component of MCMC algorithms that improves sampling efficiency by facilitating exploration of geometrically complex target distributions through an invertible map. While linear preconditioners are often sufficient…
Trimming is a ubiquitous operation in computer-aided-design whereby parts of a geometry are merged, intersected, or simply discarded. While it grants virtually unlimited flexibility in geometric design, it introduces a plethora of other…
A CUR approximation of a matrix $A$ is a particular type of low-rank approximation $A \approx C U R$, where $C$ and $R$ consist of columns and rows of $A$, respectively. One way to obtain such an approximation is to apply column subset…