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Perturbation Analysis of Moore-Penrose Metric Generalized Inverse of Linear Operators in Banach Space

Author: SunShuang
Tutor: WangYuWen
School: Harbin Normal University
Course: Applied Mathematics
Keywords: Banach space Bounded linear operators Metric Generalized Inverse Disturbance Error Estimate Bounds
CLC: O177.2
Type: Master's thesis
Year: 2010
Downloads: 42
Quote: 0
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Abstract


Banach space of bounded linear operators generalized inverse perturbation analysis play a very important role in the practical applications of operator theory , and has been widely used in statistics, optimization , control and other disciplines . Metric Generalized Inverse generally bounded homogeneous of nonlinear operator , so completely different perturbation theorem and linear generalized inverse perturbation theorem in this paper, we further study the Banach space of bounded linear operators Moore - Penrose ( single-valued ) metric generalized inverse perturbation analysis . metric Generalized Inverse of the form under certain conditions ( single-valued ) , and under such conditions the norm estimates and error bounds . applied first to measure the stable definition of disturbance and generalized orthogonal decomposition theorem is given under certain conditions of bounded linear operators Moore-Penrose single - valued metric generalized inverse error bounds , and deduced metric Generalized Inverse disturbance norm estimated next in the above theorem based on the application of the continuity of the metric projection operator and the metric generalized inverse operators may wish to add the Moore-Penrose single - valued metric generalized inverse form, and its stable disturbance norm estimates and error estimates . This article discusses only a single-valued Banach bounded linear operators measure the norm of the perturbation of the generalized inverse estimates and error estimation sector for the stability of the single- valued metric generalized inverse perturbation equivalent conditions set valued metric generalized inverse disturbance pending further investigation .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > Banach spaces and their linear operator theory.
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