Principal component analysis-based two-dimensional (PCA2D) correlation spectroscopy, combined with the eigenvalue manipulating transformation (EMT) of a spectral data set, was applied to the temperature-dependent IR spectra of poly(hydroxybutylate) (PHB). In asynchronous PCA2D correlation spectrum, we clearly captured the existence of two components in the crystalline band of the C=O stretching...

Principal component analysis (PCA) is a ubiquitous method of multivariate statistics that focuses on the eigenvalues lambda and eigenvectors of the sample covariance matrix of a data set. We consider p, N-dimensional data vectors xi drawn from a distribution with covariance matrix C. We use the replica method to evaluate the expected eigenvalue distribution rho(lambda) as N--> infinity with p=a...

Let A and B be nonnegative matrices. A new upper bound on the spectral radius ρ(A◦B) is obtained. Meanwhile, a new lower bound on the smallest eigenvalue q(A B) for the Fan product, and a new lower bound on the minimum eigenvalue q(B ◦A−1) for the Hadamard product of B and A−1 of two nonsingular M -matrices A and B are given. Some results of comparison are also given in theory. To illustrate ou...

Encouraged by the AdS/CFT correspondence, we study emergent local geometry in large N multi-matrix models from the perspective of a strong coupling expansion. By considering various solvable interacting models we show how the emergence or nonemergence of local geometry at strong coupling is captured by observables that effectively measure the mass of off-diagonal excitations about a semiclassic...

We consider the spectrum associated with the linear operator obtained when a Cahn–Hilliard system on R is linearized about a transition wave solution. In many cases it’s possible to show that the only non-negative eigenvalue is λ = 0, and so stability depends entirely on the nature of this neutral eigenvalue. In such cases, we identify a stability condition based on an appropriate Evans functio...

The vibration response of isotropic and orthotropic plates with mixed boundary conditions is numerically modeled using a solution that is based on the differential quadrature method (DQM). The DQM is applied to each region and with the imposition of appropriate boundary conditions; the problem is transformed into a standard eigenvalue problem. The δ technique is used to treat the various bounda...

We show that the quadratic matrix equation VW + η(W )W = I, for given V with positive real part and given analytic mapping η with some positivity preserving properties, has exactly one solution W with positive real part. Also we provide and compare numerical algorithms based on the iteration underlying our proofs. This work bears on operator-valued free probability theory, in particular on the ...

The purpose of this paper is to show that the joint numerical range of am-tuple of n×n hermitian matrices is convex whenever the largest eigenvalue of an associated family of hermitian matrices parameterized by the (m − 1)-dimensional sphere has constant multiplicity and, as a more technical condition, the union over the sphere of the largest eigenvalue eigenspaces does not fill the full n-dime...

We investigate the numerical computation of Maaß cusp forms for the modular group corresponding to large eigenvalues. We present Fourier coefficients of two cusp forms whose eigenvalues exceed r = 40000. These eigenvalues are the largest that have so far been found in the case of the modular group. They are larger than the 130millionth eigenvalue.

In this paper, we study numerical approximations of eigenvalues when using projection method for spectral approximations of completely continuous operators. We improve the theory depending on the ascent of T − μ and provide a new approach for error estimate, which depends only on the ascent of Th − μh. Applying this estimator to the integral operator eigenvalue problems, we obtain asymptoticall...