Implicit gamma theorems. I: Pseudoroots and pseudospectra
type: Item
instance of: scholarly article
title: Implicit gamma theorems. I: Pseudoroots and pseudospectra
zbMATH Open document ID: 1036.65048
author: Jean-Pierre Dedieu
author: Myong-Hi Kim
author: Michael Shub
author: Françoise Tisseur
published in: Foundations of Computational Mathematics
publication date: 2003-01-01T00:00:00Z
review text: Consider the analytic map \(g:E\rightarrow F\) between two Hilbert spaces, where \(g(x)\) is the solution of an equation which depends on the parameter \(x\). The authors study the \(\varepsilon\)-pseudosolutions, \(g\left( B\left( x,\varepsilon \right) \right) \), where \(B\left( x,\varepsilon \right) \) is a ball about \(x\) and of radius \(\varepsilon\). The objective here is to estimate the size of the set \(g\left( B\left( x,\varepsilon \right) \right) \) by using the derivative \(Dg(x).\) The results are applied to the implicit function map and to the polynomial eigenvalue problem.
reviewed by: Amin Boumenir
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47J10
zbMATH DE Number: 1942714
zbMATH Keywords: pseudoroots
zbMATH Keywords: pseudospectra
zbMATH Keywords: implicit gamma theorems
zbMATH Keywords: Hilbert spaces
zbMATH Keywords: pseudosolutions
zbMATH Keywords: implicit function map
zbMATH Keywords: polynomial eigenvalue problem
MaRDI profile type: Publication
full work available at URL: s10208-001-0049-z
OpenAlex ID: W2084435459
DOI: 10.1007/S10208-001-0049-Z
description: scientific article; zbMATH DE number 1942714