相关论文: Fast Computation of Sep$_\lambda$ via Interpolatio…

We revisit the non-preemptive speed-scaling problem, in which a set of jobs have to be executed on a single or a set of parallel speed-scalable processor(s) between their release dates and deadlines so that the energy consumption to be…

We present a family of fast pseudo-approximation algorithms for the minimum balanced vertex separator problem in a graph. Given a graph $G=(V,E)$ with $n$ vertices and $m$ edges, and a (constant) balance parameter $c\in(0,1/2)$, where $G$…

Given a nonlinear matrix-valued function $F(\lambda)$ and approximate eigenpairs $(\lambda_i, v_i)$, we discuss how to determine the smallest perturbation $\delta F$ such that $[F + \delta F](\lambda_i) v_i = 0$; we call the distance…

We study the weak call-by-value $\lambda$-calculus as a model for computational complexity theory and establish the natural measures for time and space -- the number of beta-reductions and the size of the largest term in a computation -- as…

The generalized eigenvalue problem (GEP) serves as a cornerstone in a wide range of applications in numerical linear algebra and scientific computing. However, traditional approaches that aim to maximize the classical Rayleigh quotient…

The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be solved…

In this paper we generalize the technique of deflation to define two new methods to systematically find many local minima of a nonlinear least squares problem. The methods are based on the Gauss-Newton algorithm, and as such do not require…

We study the generalized finite element methods (GFEMs) for the second-order elliptic eigenvalue problem with an interface in 1D. The linear stable generalized finite element methods (SGFEM) were recently developed for the elliptic source…

In this paper, we present a generalized Cuppen's divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem. We extend the Cuppen's work to the rank two modifications of the form $A =T +\beta_1\bw_1\bw_1^T +…

Spectral Embedding (SE) is a popular method for dimensionality reduction, applicable across diverse domains. Nevertheless, its current implementations face three prominent drawbacks which curtail its broader applicability: generalizability…

In this article, we present two new greedy algorithms for the computation of the lowest eigenvalue (and an associated eigenvector) of a high-dimensional eigenvalue problem, and prove some convergence results for these algorithms and their…

We consider the following interpolation problem. Suppose one is given a finite set $E \subset \mathbb{R}^d$, a function $f: E \rightarrow \mathbb{R}$, and possibly the gradients of $f$ at the points of $E$. We want to interpolate the given…

The spectrum of a network or graph $G=(V,E)$ with adjacency matrix $A$, consists of the eigenvalues of the normalized Laplacian $L= I - D^{-1/2} A D^{-1/2}$. This set of eigenvalues encapsulates many aspects of the structure of the graph,…

In this paper, we consider the problem of finding the center $Q^\ast$ of the SEB (smallest enclosing ball) for $n$ points in $d$-dimensional Euclidean space. One application of the SEB is SVDD (support vector data description) in support…

Let $G=(V,E)$ be a simple, connected graph. One is often interested in a short path between two vertices $u,v$. We propose a spectral algorithm: construct the function $\phi:V \rightarrow \mathbb{R}_{\geq 0}$ $$ \phi = \arg\min_{f:V…

Applications related to artificial intelligence, machine learning, and system identification simulations essentially use eigenvectors. Calculating eigenvectors for very large matrices using conventional methods is compute-intensive and…

The FastECPP algorithm is currently the fastest approach to prove theprimality of general numbers, and has the additional benefit of creatingcertificates that can be checked independently and with a lower complexity.This article shows how…

We develop numerical algorithms to approximate positive solutions of elliptic boundary value problems with superlinear subcritical nonlinearity on the boundary of the form $-\Delta u + u = 0$ in $\Omega$ with $\frac{\partial u}{\partial…

A new Approximate Bayesian Computation (ABC) algorithm for Bayesian updating of model parameters is proposed in this paper, which combines the ABC principles with the technique of Subset Simulation for efficient rare-event simulation, first…

Approximating the $k$-th spectral gap $\Delta_k=|\lambda_k-\lambda_{k+1}|$ and the corresponding midpoint $\mu_k=\frac{\lambda_k+\lambda_{k+1}}{2}$ of an $N\times N$ Hermitian matrix with eigenvalues…