Projectors and Projection Methods

1. Front Matter

   Pages i-ix

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2. Supplements for Linear Algebra

   • Aurél Galántai

   Pages 1-36

3. Projections

   • Aurél Galántai

   Pages 37-82

4. Finite Projection Methods for Linear Systems

   • Aurél Galántai

   Pages 83-115

5. Iterative Projection Methods for Linear Algebraic Systems

   • Aurél Galántai

   Pages 117-153

6. Projection Methods for Nonlinear Algebraic Equations

   • Aurél Galántai

   Pages 155-180

7. Projection Methods in Optimization

   • Aurél Galántai

   Pages 181-213

8. Projection Methods for Linear Equations in Hilbert Spaces

   • Aurél Galántai

   Pages 215-263

9. Back Matter

   Pages 265-287

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The projectors are considered as simple but important type of matrices and operators. Their basic theory can be found in many books, among which Hal­ 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 meth­ 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 mathemati­ 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 non­ linear systems of algebraic equations and convex optimization problems.

• Mathematica
• algebra
• functional analysis
• linear algebra
• optimization
• matrix theory

From the reviews:

"The author presents an excellent unified survey of projectors and projection methods, including the most recent results. … There is an extensive bibliography. This book fills a much needed of an excellent survey of old and new results in the area." (R. P. Tewarson, Zentralblatt MATH, Vol. 1055 (6), 2005)

• Institute of Mathematics, University of Miskolc, Hungary

  Aurél Galántai

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