The trust{region subproblem arises frequently in linear algebra and optimization applications. Recently, matrix{free methods have been introduced to solve large{ scale trust{region subproblems. These methods only require a matrix{vector product and do not rely on matrix factorizations 4, 7]. These approaches recast the trust{ region subproblem in terms of a parameterized eigenvalue problem and ...

The results of minimal model calculations indicate that the stability and the kinetic accessibility of the native state of small globular proteins are controlled by few "hot" sites. By means of molecular dynamics simulations around the native conformation, which describe the protein and the surrounding solvent at the all-atom level, an accurate and compact energetic map of the native state of t...

In this paper, some important spectral characterizations of symmetric nonnegative tensors are analyzed. In particular, it is shown that a symmetric nonnegative tensor has the following properties: (i) its spectral radius is zero if and only if it is a zero tensor; (ii) it is weakly irreducible (respectively, irreducible) if and only if it has a unique positive (respectively, nonnegative) eigenv...

Rate-splitting multiple access (RSMA) is a general scheme for downlink multi-antenna systems embracing both classical spatial division and more recent non-orthogonal access. Finding linear precoding strategy that maximizes the sum spectral efficiency of RSMA challenging yet significant problem. In this paper, we put forth novel precoder design framework jointly finds precoders common private me...

In this paper, we propose a new method to obtain the eigenvalues and fuzzy triangular eigenvectors of matrix $$\left( {\tilde{A}} \right)$$ , where elements are given. For purpose, solve 1-cut eigenvectors. Considering interval system $$\left[ \right]_{\alpha } \left[ {\tilde{X}} = {\tilde{\lambda }} 0 \le \alpha 1$$ as α-cut $$\tilde{A}\tilde{X} \tilde{\lambda }\tilde{X}$$ determine left right...

In the analytic hierarchy process (AHP), the consistency of pairwise comparison is measured by the consistency index (CI) value of pairwise comparison matrices. The CI value is defined by the size and the principal eigenvalue of comparison matrix, and the larger the CI value is, the less consistent pairwise comparison is. In this paper, we propose the estimation method of consistency intervals,...

We consider the linear growth and fragmentation equation ∂ ∂t u(x, t) + ∂ ∂x ( τ(x)u ) + β(x)u = 2 ∫ ∞ x β(y)κ(x, y)u(y, t) dy, with general coefficients τ, β and κ. Under suitable conditions (see [17]), the first eigenvalue represents the asymptotic growth rate of solutions, also called the fitness or Malthus coefficient in population dynamics. This value is of crucial importance in understand...

The recursively-constructed family of Mandelbrot matrices $M_n$ for $n=1$, $2$, $\ldots$ have nonnegative entries (indeed just $0$ and $1$, so each can be called a binary matrix) eigenvalues whose negatives $-\lambda = c$ give periodic orbits under the iteration, namely $z_k z_{k-1}^2+c$ with $z_0=0$, are thus contained in set. By Perron--Frobenius theorem, dominant real positive eigenvalue, wh...

ABSTRACT. The plane waveguides with corners considered here are infinite V-shaped strips with constant thickness. They are parametrized by their sole opening angle. We study the eigenpairs of the Dirichlet Laplacian in such domains when this angle tends to 0. We provide multi-scale asymptotics for eigenpairs associated with the lowest eigenvalues. For this, we investigate the eigenpairs of a on...