Joshua Pickard,Can Chen,Cooper Stansbury et al.
Joshua Pickard et al.
Hypergraphs and tensors extend classic graph and matrix theory to account for multiway relationships, which are ubiquitous in engineering, biological, and social systems. While the Kronecker product is a potent tool for analyzing the coupli...
ANALYTICAL SINGULAR VALUE DECOMPOSITION FOR A CLASS OF STOICHIOMETRY MATRICES [0.03%]
一类反应计量矩阵的解析奇异值分解
Jacqueline Wentz,Jeffrey C Cameron,David M Bortz
Jacqueline Wentz
We present the analytical singular value decomposition of the stoichiometry matrix for a spatially discrete reaction-diffusion system. The motivation for this work is to develop a matrix decomposition that can reveal hidden spatial flux pat...
ORTHOGONAL TRACE-SUM MAXIMIZATION: APPLICATIONS, LOCAL ALGORITHMS, AND GLOBAL OPTIMALITY [0.03%]
正交迹和最大化：应用、局部算法和全局最优性
Joong-Ho Won,Hua Zhou,Kenneth Lange
Joong-Ho Won
This paper studies the problem of maximizing the sum of traces of matrix quadratic forms on a product of Stiefel manifolds. This orthogonal trace-sum maximization (OTSM) problem generalizes many interesting problems such as generalized cano...
NEWTON CORRECTION METHODS FOR COMPUTING REAL EIGENPAIRS OF SYMMETRIC TENSORS [0.03%]
求解对称张量实特征对的Newton校正法
Ariel Jaffe,Roi Weiss,Boaz Nadler
Ariel Jaffe
Real eigenpairs of symmetric tensors play an important role in multiple applications. In this paper we propose and analyze a fast iterative Newton-based method to compute real eigenpairs of symmetric tensors. We derive sufficient conditions...
Ilse C F Ipsen,Hua Zhou
Ilse C F Ipsen
Probabilistic models are proposed for bounding the forward error in the numerically computed inner product (dot product, scalar product) between two real n-vectors. We derive probabilistic perturbation bounds as well as probabilistic roundo...
Erik Thiede,Brian VAN Koten,Jonathan Weare
Erik Thiede
For many Markov chains of practical interest, the invariant distribution is extremely sensitive to perturbations of some entries of the transition matrix, but insensitive to others; we give an example of such a chain, motivated by a problem...