Diierential Properties of Eigenvalues
نویسنده
چکیده
We deene and study a directional derivative for two functions of the spectrum of an analytic matrix valued function. These are the maximum real part and the maximum modulus of the spectrum. Results are rst obtained for the roots of polynomials with analytic coeecients by way of Puiseux-Newton series. In this regard, the primary analytic tool is the so called Puiseux-Newton diagram. These results are then translated into the context of matrices. Precise results are obtained when the eigenvalues that achieve the maximum value for the function under consideration are all either nondefective or nonderogatory. In the defective derogatory cases a general lower bound for the directional derivative is given which, in particular, describes those directions in which the directional derivative attains an innnite value.
منابع مشابه
Oscillation Theory and Numerical Solution of Fourth Order Sturm-Liouville Problems
A shooting method is developed to approximate the eigenvalues and eigenfunctions of a 4th order Sturm-Liouville problem. The main tool is a miss-distance function M(), which counts the number of eigenvalues less than. The method approximates the coeecients of the diierential equation by piecewise-constant functions, which enables an exact solution to be found on each mesh interval. In order to ...
متن کاملOscillation Theory and Numerical Solution of Sixth Order Sturm-liouville Problems
Following earlier work on fourth order problems, we develop a shooting method to approximate the eigenvalues of 6th order Sturm-Liouville problems using a spectral function N() which counts the number of eigenvalues less than. This requires anòscillation' count obtained from certain solutions of the diierential equation, and we develop explicit algorithms for obtaining the exact oscillation cou...
متن کاملAsymptotic distribution of eigenvalues of the elliptic operator system
Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.
متن کاملAsymptotic Distributions of Estimators of Eigenvalues and Eigenfunctions in Functional Data
Functional data analysis is a relatively new and rapidly growing area of statistics. This is partly due to technological advancements which have made it possible to generate new types of data that are in the form of curves. Because the data are functions, they lie in function spaces, which are of infinite dimension. To analyse functional data, one way, which is widely used, is to employ princip...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1991