Non Linear Eigenvalue Problems

نویسنده

  • Didier Robert
چکیده

In this paper we consider generalized eigenvalue problems for a family of operators with a polynomial dependence on a complex parameter. This problem is equivalent to a genuine non self-adjoint operator. We discuss here existence of non trivial eigenstates for models coming from analytic theory of smoothness for P.D.E. We shall review some old results and present recent improvements on this subject.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A New Inexact Inverse Subspace Iteration for Generalized Eigenvalue Problems

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

متن کامل

Elliptic and hyperbolic quadratic eigenvalue problems and associated distance problems

Two important classes of quadratic eigenvalue problems are composed of elliptic and hyperbolic problems. In [Linear Algebra Appl., 351–352 (2002) 455], the distance to the nearest non-hyperbolic or non-elliptic quadratic eigenvalue problem is obtained using a global minimization problem. This paper proposes explicit formulas to compute these distances and the optimal perturbations. The problem ...

متن کامل

Continuation and path following

The main ideas of path following by predictor-corrector and piecewise-linear methods, and their application in the direction of homotopy methods and non-linear eigenvalue problems are reviewed. Further new applications to areas such as polynomial systems of equations, linear eigenvalue problems, interior methods for linear programming, parametric programming and complex bifurcation are surveyed...

متن کامل

Solving Large-scale Eigenvalue Problems in SciDAC Applications

Large-scale eigenvalue problems arise in a number of DOE applications. This paper provides an ovcrvicw of thc recent dcvclopriicrit of cigciivaluc computation in the coritcxt of two SciDAC applications. We emphasize the importance of Krylov suhspace methods, and point out its limitations. M7e discuss the value of alternative approaches that are more amenable to the use of prcconditioncrs, arid ...

متن کامل

An Enhanced Fictitious Time Integration Method for Non-Linear Algebraic Equations With Multiple Solutions: Boundary Layer, Boundary Value and Eigenvalue Problems

When problems in engineering and science are discretized, algebraic equations appear naturally. In a recent paper by Liu and Atluri, non-linear algebraic equations (NAEs) were transformed into a nonlinear system of ODEs, which were then integrated by a method labelled as the Fictitious Time Integration Method (FTIM). In this paper, the FTIM is enhanced, by using the concept of a repellor in the...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004