For generalized eigenvalue problems, we consider computing all eigenvalues located in a certain region and their corresponding eigenvectors. Recently, contour integral spectral projection methods have been proposed for such problems. In this study, from an analysis of the relationship between the contour integral spectral projection and the Krylov subspace, we provide a novel interpretation of ...

Cauchy principal value is a standard method applied in mathematical applications by which an improper, and possibly divergent, integral is measured in a balanced way around singularities or at infinity. On the other hand, entropy prediction of systems behavior from a thermodynamic perspective commonly involves contour integrals. With the aim of facilitating the calculus of such integrals in thi...

A contour gauge of general type is analysed where 1-form (vector potential) is expressed as a contour integral of the 2-form (field strength) along an arbitrary contour C. For a special class of contours the gauge condition reduces to k µ (x)A µ (x) = 0 where k µ (x) is a tangent vector to the contour C. It is shown, that this gauge is advantageous to give a simple proof of the nonabelian Stoke...

This paper develops an approach to the evaluation of Euler sums involving harmonic numbers either linearly or nonlinearly. We give explicit formull for certain classes of Euler sums in terms of values of the Riemann zeta function at positive integers. The approach is based on simple contour integral representations and residue computations. Sommes d'Euler et repr esentations int egrales R esum ...

An extension of the contour integral method (CIM) for the computation of stress intensity factors for loaded cracks is presented. Numerical solutions of the two-dimensional linear elasticity equations are computed with the p-version of the generalized finite element method. Polynomial enrichment functions as well as enrichment with near crack tip asymptotic expansion are used. The robustness of...

In this paper we express the disentangling, or the formation of a function of several noncommuting operators using Cauchy’s Integral Formula in several complex variables. It is seen that the disentangling of a given function f can be expressed as a contour integral around the boundary of a polydisk where the standard Cauchy kernel is replaced by the disentangling of the Cauchy kernel expressed ...

Contour error reduction for modern machining processes is an important concern in multi-axis contour tracking applications in order to ensure the quality of final products. Many control methods were developed in time domain to deal with contour tracking problems, and a proportional–derivative (PD) position domain control (PDC) was also proposed by the authors. It is well known that proportional...

Abstract We generalize ideas in the recent literature and develop new ones order to propose a general class of contour integral methods for linear convection–diffusion PDEs particular those arising finance. These aim provide numerical approximation solution by computing its inverse Laplace transform. The choice integration is determined computation few suitably weighted pseudo-spectral level se...

We develop an analytical approach for the study of the quench dynamics of the anisotropic Heisenberg model (XXZ model) on the infinite line. We present the exact time-dependent wave functions after a quench in an integral form for any initial state and for any anisotropy Δ by means of a generalized Yudson contour representation. We calculate the evolution of several observables from two particu...