Faber Polynomials of Matrices for Non-convex Sets
نویسنده
چکیده
It has been recently shown that ||Fn(A)|| ≤ 2, where A is a linear continuous operator acting in a Hilbert space, and Fn is the Faber polynomial of degree n corresponding to some convex compact E ⊂ C containing the numerical range of A. Such an inequality is useful in numerical linear algebra, it allows for instance to derive error bounds for Krylov subspace methods. In the present paper we extend this result to not necessary convex sets E.
منابع مشابه
Zeros and Local Extreme Points of Faber Polynomials Associated with Hypocycloidal Domains∗
Faber polynomials play an important role in different areas of constructive complex analysis. Here, the zeros and local extreme points of Faber polynomials for hypocycloidal domains are studied. For this task, we use tools from linear algebra, namely, the Perron-Frobenius theory of nonnegative matrices, the Gantmacher-Krein theory of oscillation matrices, and the Schmidt-Spitzer theory for the ...
متن کاملArnoldi-Faber method for large non hermitian eigenvalue problems
We propose a restarted Arnoldi’s method with Faber polynomials and discuss its use for computing the rightmost eigenvalues of large non hermitian matrices. We illustrate, with the help of some practical test problems, the benefit obtained from the Faber acceleration by comparing this method with the Chebyshev based acceleration. A comparison with the implicitly restarted Arnoldi method is also ...
متن کاملCoefficient Estimates for a General Subclass of m-fold Symmetric Bi-univalent Functions by Using Faber Polynomials
In the present paper, we introduce a new subclass H∑m (λ,β)of the m-fold symmetric bi-univalent functions. Also, we find the estimates of the Taylor-Maclaurin initial coefficients |am+1| , |a2m+1| and general coefficients |amk+1| (k ≥ 2) for functions in this new subclass. The results presented in this paper would generalize and improve some recent works of several earlier authors.
متن کاملOn Chebyshev Polynomials of Matrices
The mth Chebyshev polynomial of a square matrix A is the monic polynomial that minimizes the matrix 2-norm of p(A) over all monic polynomials p(z) of degree m. This polynomial is uniquely defined if m is less than the degree of the minimal polynomial of A. We study general properties of Chebyshev polynomials of matrices, which in some cases turn out to be generalizations of well known propertie...
متن کاملBernstein's polynomials for convex functions and related results
In this paper we establish several polynomials similar to Bernstein's polynomials and several refinements of Hermite-Hadamard inequality for convex functions.
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 2013