Related papers: Block Iterative Eigensolvers for Sequences of Corr…
The paper describes several efficient parallel implementations of the one-sided hyperbolic Jacobi-type algorithm for computing eigenvalues and eigenvectors of Hermitian matrices. By appropriate blocking of the algorithms an almost ideal…
Preconditioned iterative methods for numerical solution of large matrix eigenvalue problems are increasingly gaining importance in various application areas, ranging from material sciences to data mining. Some of them, e.g., those using…
We propose a novel method for the efficient and accurate iterative solution of frequency domain integral equations (IEs) that are used for large/multi-scale electromagnetic scattering problems. The proposed method uses a novel…
Recently, a new eigenvalue problem, called the transmission eigenvalue problem, has attracted many researchers. The problem arose in inverse scattering theory for inhomogeneous media and has important applications in a variety of inverse…
The linear response eigenvalue problem, which arises from many scientific and engineering fields, is quite challenging numerically for large-scale sparse/dense system, especially when it has zero eigenvalues. Based on a direct sum…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
Consider $n$ linearly independent vectors in $\mathbb{C}^n$ which form columns of a matrix $A$. The recursive evaluation of eigen directions (normalized eigenvectors) of $A$ is the solution of an eigenvalue problem of the form…
Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…
In this work we are interested in general linear inverse problems where the corresponding forward problem is solved iteratively using fixed point methods. Then one-shot methods, which iterate at the same time on the forward problem solution…
Block-structured integer linear programs (ILPs) play an important role in various application fields. We address $n$-fold ILPs where the matrix $\mathcal{A}$ has a specific structure, i.e., where the blocks in the lower part of…
We present an alternative procedure for solving the eigenvalue problem of replicated transfer matrices describing disordered spin systems with (random) 1D nearest neighbor bonds and/or random fields, possibly in combination with (random)…
This paper investigates a class of non-autonomous highly oscillatory ordinary differential equations characterized by a linear component inversely proportional to a small parameter $\varepsilon$, with purely imaginary eigenvalues, and an…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
The nonzero eigenvalues of $AB$ are equal to those of $BA$: an identity that holds as long as the products are square, even when $A,B$ are rectangular. This fact naturally suggests an efficient algorithm for computing eigenvalues and…
A new approach is discussed for solving large nonsymmetric systems of linear equations with multiple right-hand sides. The first system is solved with a deflated GMRES method that generates eigenvector information at the same time that the…
We propose a general modeling and algorithmic framework for discrete structure recovery that can be applied to a wide range of problems. Under this framework, we are able to study the recovery of clustering labels, ranks of players, signs…
We propose a general framework to study the stability of the subspace spanned by $P$ consecutive eigenvectors of a generic symmetric matrix ${\bf H}_0$, when a small perturbation is added. This problem is relevant in various contexts,…
We show that the joint spectral radius of a finite collection of nonnegative matrices can be bounded by the eigenvalue of a non-linear operator. This eigenvalue coincides with the ergodic constant of a risk-sensitive control problem, or of…
Motivated by the recent demonstration of its use as a tool for the detection and characterization of phase-shape correlations in multivariate time series, we show that eigenvalue decomposition can also be applied to a matrix of indices of…
An a posteriori verification method is proposed for the generalized real-symmetric eigenvalue problem and is applied to densely clustered eigenvalue problems in large-scale electronic state calculations. The proposed method is realized by a…