相关论文: An Inverse-free Truncated Rayleigh-Ritz Method for…
Recently, Krukier et al. [Generalized skew-Hermitian triangular splitting iteration methods for saddle-point linear systems, Numer. Linear Algebra Appl. 21 (2014) 152-170] proposed an efficient generalized skew-Hermitian triangular…
We develop an iterative refinement method that improves the accuracy of a user-chosen subset of $k$ eigenvectors ($k\ll n$) of an $n\times n$ real symmetric matrix. Using an orthogonal matrix represented in compact WY form, the method…
Sparse principal component analysis with global support (SPCAgs), is the problem of finding the top-$r$ leading principal components such that all these principal components are linear combinations of a common subset of at most $k$…
In this paper, we address \ac{SGNEP} seeking with risk-neutral agents. Our main contribution lies the development of a stochastic variance-reduced gradient (SVRG) technique, modified to contend with general sample spaces, within a…
In this paper a new approach for constructing \emph{multivariate} Gaussian random fields (GRFs) using systems of stochastic partial differential equations (SPDEs) has been introduced and applied to simulated data and real data. By solving a…
Sliced Inverse Regression (SIR) is an effective method for dimension reduction in high-dimensional regression problems. The original method, however, requires the inversion of the predictors covariance matrix. In case of collinearity…
We study the generalized forward-reflected-backward (GFRB) method, an extension of the forward-reflected-backward (FRB) scheme due to Malitsky and Tam, for solving monotone inclusion problems in real Hilbert spaces. We first analyze GFRB…
This work deals with approximate solution of generalized eigenvalue problem with coefficient matrix that is an affine function of d-parameters. The coefficient matrix is assumed to be symmetric positive definite and spectrally equivalent to…
Over the past decade, stochastic algorithms have emerged as scalable and efficient tools for solving large-scale ill-posed inverse problems by randomly selecting subsets of equations at each iteration. However, due to the ill-posedness and…
We present a comprehensive convergence analysis for Self-Consistent Field (SCF) iteration to solve a class of nonlinear eigenvalue problems with eigenvector-dependency (NEPv). Using a tangent-angle matrix as an intermediate measure for…
Large-scale association analysis between multivariate responses and predictors is of great practical importance, as exemplified by modern business applications including social media marketing and crisis management. Despite the rapid…
Supervised dimensionality reduction strategies have been of great interest. However, current supervised dimensionality reduction approaches are difficult to scale for situations characterized by large datasets given the high computational…
Generalized inverses play a fundamental role in numerical linear algebra, particularly when matrices are rectangular, singular, or rank deficient. Even when the input matrix is sparse, generalized inverses such as the M-P pseudoinverse are…
We consider the estimation of parameter-dependent statistics of functional outputs of elliptic boundary value problems (BVPs) with parametrized random and deterministic inputs. For a given value of the deterministic paremeter, a stochastic…
Shuffling gradient methods are widely used in modern machine learning tasks and include three popular implementations: Random Reshuffle (RR), Shuffle Once (SO), and Incremental Gradient (IG). Compared to the empirical success, the…
Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications,…
Recently, a kind of eigensolvers based on contour integral were developed for computing the eigenvalues inside a given region in the complex plane. The CIRR method is a classic example among this kind of methods. In this paper, we propose a…
A major enterprise in compressed sensing and sparse approximation is the design and analysis of computationally tractable algorithms for recovering sparse, exact or approximate, solutions of underdetermined linear systems of equations. Many…
Few-shot learning (FSL), purposing to resolve the problem of data-scarce, has attracted considerable attention in recent years. A popular FSL framework contains two phases: (i) the pre-train phase employs the base data to train a CNN-based…
Many computer vision applications require robust and efficient estimation of camera geometry. The robust estimation is usually based on solving camera geometry problems from a minimal number of input data measurements, i.e. solving minimal…