相关论文: Fast non-Hermitian Toeplitz eigenvalue computation…

Let $a(z)=\sum_{i\in\mathbb Z}a_iz^i$ be a complex valued continuous function, defined for $|z|=1$, such that $\sum_{i=-\infty}^{+\infty}|ia_i|<\infty$. Consider the semi-infinite Toeplitz matrix $T(a)=(t_{i,j})_{i,j\in\mathbb Z^+}$…

We study the problem of nonparametric estimation of the linear multiplier function $\theta(t)$ for processes satisfying stochastic differential equations of the type $$dX_t=\theta(t) X_tdt+ \epsilon dZ^{q,H}_t, X_0=x_0, 0\leq t \leq T$$…

We consider an $N \times N$ random symmetric Toeplitz matrix with an i.i.d. input sequence drawn from a distribution that lies in the domain of attraction of an $\alpha$-stable law for $0 < \alpha < 2$. We show that under an appropriate…

We develop an analytic theory of operator-valued additive free convolution in terms of subordination functions. In contrast to earlier investigations our functions are not just given by power series expansions, but are defined as Frechet…

We consider the transmission eigenvalue problem for an impenetrable obstacle with Dirichlet boundary condition surrounded by a thin layer of non-absorbing inhomogeneous material. We derive a rigorous asymptotic expansion for the first…

The main difficulty in solving the Helmholtz equation within polygons is due to non-analytic vertices. By using a method nearly identical to that used by Fox, Henrici, and Moler in their 1967 paper; it is demonstrated that such eigenvalue…

We present general prescriptions for the asymptotic expansion of massive multi-loop Feynman integrals near threshold. As in the case of previously known prescriptions for various limits of momenta and masses, the terms of the threshold…

In a domain $\Omega\subset \mathbb{R}^{\mathbf{N}}$ we consider a selfadjoint operator $\mathbf{T}=\mathfrak{A}^*P\mathfrak{A} ,$ where $\mathfrak{A}$ is a pseudodifferential operator of order $-l=-\mathbf{N}/2$ and $P=V\mu_{\Sigma}$ is a…

In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image-processing, graph partition and classification, nonlinear physics and more. The canonical eigenproblem we…

We study random matrices acting on tensor product spaces which have been transformed by a linear block operation. Using operator-valued free probability theory, under some mild assumptions on the linear map acting on the blocks, we compute…

We initiate a study of asymptotic Toeplitz operators on the Hardy space $H^2(\mathbb{D}^n)$ (over the unit polydisc $\mathbb{D}^n$ in $\mathbb{C}^n$). We also study the Toeplitz operators in the polydisc setting. Our main results on…

A new algorithm for eigenvalue problems for the fractional Jacobi type ODE is proposed. The algorithm is based on piecewise approximation of the coefficients of the differential equation with subsequent recursive procedure adapted from some…

We calculate the eigenvalues of some two-dimensional non-Hermitian Hamiltonians by means of a pseudospectral method and straightforward diagonalization of the Hamiltonian matrix in a suitable basis set. Both sets of results agree remarkably…

Two-term asymptotic formulae for the probability distribution functions for the smallest eigenvalue of the Jacobi $ \beta $-Ensembles are derived for matrices of large size in the r\'egime where $ \beta > 0 $ is arbitrary and one of the…

Stochastic optimisation in Riemannian manifolds, especially the Riemannian stochastic gradient method, has attracted much recent attention. The present work applies stochastic optimisation to the task of recursive estimation of a…

In this paper we study spectral properties of non-selfadjoint operators with the discrete spectrum. The main challenge is to represent a complete description of belonging to the Schatten class through the properties of the Hermitian real…

We discuss the program EXP used to automate the successive application of asymptotic expansions to Feynman diagrams. We focus on the generation of the relevant subgraphs and the determination of the topologies for the remaining integrals.…

The eigenvalues of the Hatano--Nelson non-Hermitian Anderson matrices, in the spectral regions in which the Lyapunov exponent exceeds the non-Hermiticity parameter, are shown to be real and exponentially close to the Hermitian eigenvalues.…

We present a method, based on loop equations, to compute recursively, all the terms in the large $N$ topological expansion of the free energy for the 2-hermitian matrix model, in the case where the support of the density of eigenvalues is…

This paper aims to study the asymptotic expansion of analytic torsion forms associated with a certain series of flat bundles. We prove the existence of the full expansion and give a formula for the sub-leading term, while Bismut-Ma-Zhang…