Related papers: Performance of Refined Isogeometric Analysis in So…
The solution of eigenproblems is often a key computational bottleneck that limits the tractable system size of numerical algorithms, among them electronic structure theory in chemistry and in condensed matter physics. Large eigenproblems…
This paper considers the sparse generalized eigenvalue problem (SGEP), which aims to find the leading eigenvector with at most $k$ nonzero entries. SGEP naturally arises in many applications in machine learning, statistics, and scientific…
Matrix exponential discriminant analysis (EDA) is a generalized discriminant analysis method based on matrix exponential. It can essentially overcome the intrinsic difficulty of small sample size problem that exists in the classical linear…
In electronic structure calculations, various material properties can be obtained by means of computing the total energy of a system as well as derivatives of the total energy w.r.t. atomic positions. The derivatives, also known as…
In fields ranging from computer vision to signal processing and statistics, increasing computational power allows a move from classical linear models to models that incorporate non-linear phenomena. This shift has created interest in…
Often the easiest way to discretize an ordinary or partial differential equation is by a rectangular numerical method, in which n basis functions are sampled at m>>n collocation points. We show how eigenvalue problems can be solved in this…
As a judicious correspondence to the classical maxcut, the anti-Cheeger cut has more balanced structure, but few numerical results on it have been reported so far. In this paper, we propose a continuous iterative algorithm (CIA) for the…
In Part I of this paper, we introduced a 2D eigenvalue problem (2DEVP) and presented theoretical results of the 2DEVP and its intrinsic connetion with the eigenvalue optimizations. In this part, we devise a Rayleigh quotient iteration…
Independent component analysis (ICA) aims at decomposing an observed random vector into statistically independent variables. Deflation-based implementations, such as the popular one-unit FastICA algorithm and its variants, extract the…
This work introduces a novel algorithm to solve large-scale eigenvalue problems and seek a small set of eigenpairs. The method, called randomized Krylov-Schur (rKS), has a simple implementation and benefits from fast and efficient…
Independent Component Analysis (ICA) is a popular model for blind signal separation. The ICA model assumes that a number of independent source signals are linearly mixed to form the observed signals. We propose a new algorithm, PEGI (for…
Retrieval Augmented Generation (RAG) is a common method for integrating external knowledge into pretrained Large Language Models (LLMs) to enhance accuracy and relevancy in question answering (QA) tasks. However, prompt engineering and…
We introduce a novel computational framework for the multiscale simulation of higher-order continua that allows for the consideration of first-, second- and third- order effects at both micro- and macro-level. In line with classical…
We present and analyze a new stable space-time Isogeometric Analysis (IgA) method for the numerical solution of parabolic evolution equations in fixed and moving spatial computational domains. The discrete bilinear form is elliptic on the…
A novel and efficient approach which is based on the framework of isogeometric analysis for elliptic homogenization problems is proposed. These problems possess highly oscillating coefficients leading to extremely high computational…
Fisher discriminant analysis (FDA) is a widely used method for classification and dimensionality reduction. When the number of predictor variables greatly exceeds the number of observations, one of the alternatives for conventional FDA is…
The integer factorization problem (IFP) underpins the security of RSA, yet becomes efficiently solvable on a quantum computer through Shor's algorithm. Regev's recent high-dimensional variant reduces the circuit size through lattice-based…
We introduce Riemannian Integrated Gradients (RIG); an extension of Integrated Gradients (IG) to Riemannian manifolds. We demonstrate that RIG restricts to IG when the Riemannian manifold is Euclidean space. We show that feature attribution…
Image Quality Assessment (IQA) with references plays an important role in optimizing and evaluating computer vision tasks. Traditional methods assume that all pixels of the reference and test images are fully aligned. Such Aligned-Reference…
The paper is concerned with locally stabilized space-time IgA approximations to initial boundary value problems of the parabolic type. Originally, similar schemes (but weighted with a global mesh parameter) was presented and studied by U.…