Related papers: Network analysis using Krylov subspace trajectorie…
Krylov subspace methods are a ubiquitous tool for computing near-optimal rank $k$ approximations of large matrices. While "large block" Krylov methods with block size at least $k$ give the best known theoretical guarantees, block size one…
New algorithms are proposed for the Tucker approximation of a 3-tensor, that access it using only the tensor-by-vector-by-vector multiplication subroutine. In the matrix case, Krylov methods are methods of choice to approximate the dominant…
The traffic behavior of University of Louisville network with the interconnected backbone routers and the number of Virtual Local Area Network (VLAN) subnets is investigated using the Random Matrix Theory (RMT) approach. We employ the…
Link prediction in networks is typically accomplished by estimating or ranking the probabilities of edges for all pairs of nodes. In practice, especially for social networks, the data are often collected by egocentric sampling, which means…
In this paper we develop randomized Krylov subspace methods for efficiently computing regularized solutions to large-scale linear inverse problems. Building on the recently developed randomized Gram-Schmidt process, where sketched inner…
We study the use of Krylov subspace recycling for the solution of a sequence of slowly-changing families of linear systems, where each family consists of shifted linear systems that differ in the coefficient matrix only by multiples of the…
Many network analysis and graph learning techniques are based on models of random walks which require to infer transition matrices that formalize the underlying stochastic process in an observed graph. For weighted graphs, it is common to…
Let a network be represented by a simple graph $\mathcal{G}$ with $n$ vertices. A common approach to investigate properties of a network is to use the adjacency matrix $A=[a_{ij}]_{i,j=1}^n\in\R^{n\times n}$ associated with the graph…
We apply novel inner-iteration preconditioned Krylov subspace methods to the interior-point algorithm for linear programming (LP). Inner-iteration preconditioners recently proposed by Morikuni and Hayami enable us to overcome the severe…
This paper presents a new method to determine the susceptances of a reduced transmission network representation by using nonlinear optimization. We use Power Transfer Distribution Factors (PTDFs) to convert the original grid into a reduced…
Randomized Krylov subspace methods that employ the sketch-and-solve paradigm to substantially reduce orthogonalization cost have recently shown great promise in speeding up computations for many core linear algebra tasks (e.g., solving…
We consider the solution of large stiff systems of ordinary differential equations with explicit exponential Runge--Kutta integrators. These problems arise from semi-discretized semi-linear parabolic partial differential equations on…
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…
Random networks are increasingly used to analyse complex transportation networks, such as airline routes, roads and rail networks. So far, this research has been focused on describing the properties of the networks with the help of random…
The power flow equations are non-linear multivariate equations that describe the relationship between power injections and bus voltages of electric power networks. Given a network topology, we are interested in finding network parameters…
Modeling the microstructural evolution of metal and alloys, specifically under irradiation, is essential to predict the aging properties of materials. Many models are based on a transition rate matrix describing the jump frequencies of…
The eigenvalues of matrices representing the structure of large-scale complex networks present a wide range of applications, from the analysis of dynamical processes taking place in the network to spectral techniques aiming to rank the…
Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. {While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the…
In analysis and control of large-scale nonlinear dynamical systems, a distributed approach is often an attractive option due to its computational tractability and usually low communication requirements. Success of the distributed control…
We present variants of the Conjugate Gradient (CG), Conjugate Residual (CR), and Generalized Minimal Residual (GMRES) methods which are both pipelined and flexible. These allow computation of inner products and norms to be overlapped with…