Analytic roots of invertible matrix functions
نویسندگان
چکیده
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.
منابع مشابه
Ela 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 کاملSOME REMARKS ON WEAKLY INVERTIBLE FUNCTIONS IN THE UNIT BALL AND POLYDISK
We will present an approach to deal with a problem of existence of (not) weakly invertible functions in various spaces of analytic functions in the unit ball and polydisk based on estimates for integral operators acting between functional classes of different dimensions.
متن کاملNumerical Elimination, Newton Method and Multiple Roots
Newton’s iteration has quadratic convergence for simple roots. We present a Newton-based iteration scheme with quadratic convergence for multiple roots of systems of analytic functions. This is a report on work in progress. 1. Newton Iteration, Approximate Roots and γ-Theorems 1.1. Newton Iteration. Let f : Cn → Cn be an analytic function. Newton’s method for solving f = 0 consists in approxima...
متن کاملMonodromy of Dual Invertible Polynomials
A generalization of Arnold’s strange duality to invertible polynomials in three variables by the first author and A. Takahashi includes the following relation. For some invertible polynomials f the Saito dual of the reduced monodromy zeta function of f coincides with a formal “root” of the reduced monodromy zeta function of its Berglund– Hübsch transpose f . Here we give a geometric interpretat...
متن کاملHadamard Inverses, Square Roots and Products of Almost Semidefinite Matrices
Let A = (aij) be an n × n symmetric matrix with all positive entries and just one positive eigenvalue. Bapat proved then that the Hadamard inverse of A, given by A = ( 1 aij ) is positive semidefinite. We show that if moreover A is invertible then A is positive definite. We use this result to obtain a simple proof that with the same hypotheses on A, except that all the diagonal entries of A are...
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 2017