Related papers: Inexact Krylov Subspace Algorithms for Large Matri…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
For large scale electronic structure calculation, the Krylov subspace method is introduced to calculate the one-body density matrix instead of the eigenstates of given Hamiltonian. This method provides an efficient way to extract the…
The rapid growth of circuit complexity has rendered Model Order Reduction (MOR) a key enabler for the efficient simulation of large circuit models. MOR techniques based on moment-matching are well established due to their simplicity and…
Deep learning has revolutionized the performance of classification, but meanwhile demands sufficient labeled data for training. Given insufficient data, while many techniques have been developed to help combat overfitting, the challenge…
This monograph is centred at the intersection of three mathematical topics, that are theoretical in nature, yet with motivations and relevance deep rooted in applications: the linear inverse problems on abstract, in general…
We consider the linear least squares problem with linear equality constraints (LSE problem) formulated as $\min_{x\in\mathbb{R}^{n}}\|Ax-b\|_2 \ \mathrm{s.t.} \ Cx = d$. Although there are some classical methods available to solve this…
In this paper, we present numerical methods suitable for solving convex quadratic Fractional Differential Equation (FDE) constrained optimization problems, with box constraints on the state and/or control variables. We develop an…
This paper presents a new algorithm KIOPS for computing linear combinations of $\varphi$-functions that appear in exponential integrators. This algorithm is suitable for large-scale problems in computational physics where little or no…
Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…
Eigensystem Realization Algorithm (ERA) is a data-driven approach for subspace system identification and is widely used in many areas of engineering. However, the computational cost of the ERA is dominated by a step that involves the…
Domain adaptation (DA) aims to generalize a learning model across training and testing data despite the mismatch of their data distributions. In light of a theoretical estimation of upper error bound, we argue in this paper that an…
EigenDecomposition (ED) is at the heart of many computer vision algorithms and applications. One crucial bottleneck limiting its usage is the expensive computation cost, particularly for a mini-batch of matrices in deep neural networks. Our…
We consider a Krylov subspace approximation method for the symmetric differential Riccati equation $\dot{X} = AX + XA^T + Q - XSX$, $X(0)=X_0$. The method we consider is based on projecting the large scale equation onto a Krylov subspace…
This paper describes a software package called EVSL (for EigenValues Slicing Library) for solving large sparse real symmetric standard and generalized eigenvalue problems. As its name indicates, the package exploits spectrum slicing, a…
Symbolic data analysis (SDA) aggregates large individual-level datasets into a small number of distributional summaries, such as random rectangles or random histograms. The inference is carried out using these summaries in place of the…
The bilinear form of a matrix function, namely $\mathbf{u}^\top f(A) \mathbf{v}$, appears in many scientific computing problems, where $\mathbf{u}, \mathbf{v} \in \mathbb{R}^n$, $A \in \mathbb{R}^{n \times n}$, and $f(z)$ is a given…
Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or…
We consider discrete linear Chebyshev approximation problems in which the unknown parameters of linear function are fitted by minimizing the maximum absolute deviation of errors. Such problems find application in the solution of…
Recent works in self-supervised learning have shown impressive results on single-object images, but they struggle to perform well on complex multi-object images as evidenced by their poor visual grounding. To demonstrate this concretely, we…
Seismic imaging is a major challenge in geophysics with broad applications. It involves solving wave propagation equations with absorbing boundary conditions (ABC) multiple times. This drives the need for accurate and efficient numerical…