Superoptimal Analytic Approximations of Matrix Functions
نویسندگان
چکیده
منابع مشابه
Optimal and superoptimal matrix algebra operators
We study the optimal and superoptimal Frobenius operators in a general matrix vector space and in particular in the multilevel trigonometric matrix vector spaces, by emphasizing both the algebraic and geometric properties. These general results are used to extend the Korovkin matrix theory for the approximation of block Toeplitz matrices via trigonometric vector spaces. The abstract theory is t...
متن کاملSuperoptimal Preconditioners for Functions of Matrices
For any given matrix A ∈ Cn×n, a preconditioner tU (A) called the superoptimal preconditioner was proposed in 1992 by Tyrtyshnikov [20]. It has been shown that tU (A) is an efficient preconditioner for solving various structured systems, for instance, Toeplitzlike systems. In this paper, we construct the superoptimal preconditioners for different functions of matrices. Let f be a function of ma...
متن کاملEla Analytic Roots of Invertible Matrix Functions∗
Various conditions are developed that guarantee existence of analytic roots of a given analytic matrix function with invertible values defined on a simply connected domain.
متن کاملAnalytic roots of invertible matrix functions
Various conditions are developed that guarantee existence of analytic roots of a given analytic matrix function with invertible values defined on a simply connected domain.
متن کاملAnalytic Approximation of Matrix Functions in L
We consider the problem of approximation of matrix functions of class L on the unit circle by matrix functions analytic in the unit disk in the norm of L, 2 ≤ p < ∞. For an m × n matrix function Φ in L, we consider the Hankel operator HΦ : H(C) → H −(C), 1/p + 1/q = 1/2. It turns out that the space of m × n matrix functions in L splits into two subclasses: the set of respectable matrix function...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 1994
ISSN: 0022-1236
DOI: 10.1006/jfan.1994.1034