Projectors and Projection Methods
β Scribed by AurΓ©l GalΓ‘ntai (auth.)
- Publisher
- Springer US
- Year
- 2004
- Tongue
- English
- Leaves
- 292
- Series
- Advances in Mathematics 6
- Edition
- 1
- Category
- Library
No coin nor oath required. For personal study only.
β¦ Synopsis
The projectors are considered as simple but important type of matrices and operators. Their basic theory can be found in many books, among which HalΒ mas [177], [178] are of particular significance. The projectors or projections became an active research area in the last two decades due to ideas generated from linear algebra, statistics and various areas of algorithmic mathematics. There has also grown up a great and increasing number of projection methΒ ods for different purposes. The aim of this book is to give a unified survey on projectors and projection methods including the most recent results. The words projector, projection and idempotent are used as synonyms, although the word projection is more common. We assume that the reader is familiar with linear algebra and mathematiΒ cal analysis at a bachelor level. The first chapter includes supplements from linear algebra and matrix analysis that are not incorporated in the standard courses. The second and the last chapter include the theory of projectors. Four chapters are devoted to projection methods for solving linear and nonΒ linear systems of algebraic equations and convex optimization problems.
β¦ Table of Contents
Front Matter....Pages i-ix
Supplements for Linear Algebra....Pages 1-36
Projections....Pages 37-82
Finite Projection Methods for Linear Systems....Pages 83-115
Iterative Projection Methods for Linear Algebraic Systems....Pages 117-153
Projection Methods for Nonlinear Algebraic Equations....Pages 155-180
Projection Methods in Optimization....Pages 181-213
Projection Methods for Linear Equations in Hilbert Spaces....Pages 215-263
Back Matter....Pages 265-287
β¦ Subjects
Linear and Multilinear Algebras, Matrix Theory; Numeric Computing; Algorithms; Optimization; Functional Analysis
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