Related papers: ML(n)BiCGStabt: A ML(n)BiCGStab variant with A-tra…

When an iterative method is applied to solve the linear equation system in interior point methods (IPMs), the attention is usually placed on accelerating their convergence by designing appropriate preconditioners, but the linear solver is…

Time-Resolved Spectroscopy (TRS) is a powerful modality for non-invasive characterization of turbid media. However, extracting optical properties, absorption $\mu_a$ and reduced scattering $\mu_s'$, from 3D stochastic measurements remains…

An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…

In this paper, we present a family of multivariate grid transfer operators appropriate for anisotropic multigrid methods. Our grid transfer operators are derived from a new family of anisotropic interpolatory subdivision schemes. We study…

The rapid pace of innovation in biological microscopy imaging has led to large images, putting pressure on data storage and impeding efficient sharing, management, and visualization. This necessitates the development of efficient…

In this work, we develop an $\mathcal{O}(N)$ implicit real space method in 1D and 2D for the Cahn Hilliard (CH) and vector Cahn Hilliard (VCH) equations, based on the Method Of Lines Transpose (MOL$^\text{T}$) formulation. This formulation…

Randomized iterative methods, such as the randomized Kaczmarz method, have gained significant attention for solving large-scale linear systems due to their simplicity and efficiency. Meanwhile, Krylov subspace methods have emerged as a…

This paper introduces a new class of algorithms for solving large-scale linear inverse problems based on new flexible and inexact Golub-Kahan factorizations. The proposed methods iteratively compute regularized solutions by approximating a…

Markov Chain Monte Carlo (MCMC) sampling from a posterior distribution corresponding to a massive data set can be computationally prohibitive since producing one sample requires a number of operations that is linear in the data size. In…

The paper discusses the efficiency of the classical BiCGStab method and several of its modifications for solving systems with multiple right-hand side vectors. These iterative methods are widely used for solving systems with large sparse…

Deep Learning (DL) methods can reconstruct highly accelerated magnetic resonance imaging (MRI) scans, but they rely on application-specific large training datasets and often generalize poorly to out-of-distribution data. Self-supervised…

Recently, Transformer is much popular and plays an important role in the fields of Machine Learning (ML), Natural Language Processing (NLP), and Computer Vision (CV), etc. In this paper, based on the Vision Transformer (ViT) model, a new…

Classical iterative methods for tomographic reconstruction include the class of Algebraic Reconstruction Techniques (ART). Convergence of these stationary linear iterative methods is however notably slow. In this paper we propose the use of…

Implicit Neural Representations (INRs) are widely used to encode data as continuous functions, enabling the visualization of large-scale multivariate scientific simulation data with reduced memory usage. However, existing INR-based methods…

We consider solution of multiply shifted systems of nonsymmetric linear equations, possibly also with multiple right-hand sides. First, for a single right-hand side, the matrix is shifted by several multiples of the identity. Such problems…

Models coming from different physical applications are very large in size. Simulation with such systems is expensive so one usually obtains a reduced model (by model reduction) that replicates the input-output behaviour of the original full…

Biclustering is a powerful data mining technique that allows simultaneously clustering rows (observations) and columns (features) in a matrix-format data set, which can provide results in a checkerboard-like pattern for visualization and…

We compare two approaches to compute a portion of the spectrum of dense symmetric definite generalized eigenproblems: one is based on the reduction to tridiagonal form, and the other on the Krylov-subspace iteration. Two large-scale…

We introduce an algorithm for estimating the trace of a matrix function $f(\mathbf{A})$ using implicit products with a symmetric matrix $\mathbf{A}$. Existing methods for implicit trace estimation of a matrix function tend to treat…

In this paper, we propose a novel reduced-rank adaptive filtering algorithm by blending the idea of the Krylov subspace methods with the set-theoretic adaptive filtering framework. Unlike the existing Krylov-subspace-based reduced-rank…