Algorithms for Solving Common Fixed Point Problems

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Calculus
Cover of the book Algorithms for Solving Common Fixed Point Problems by Alexander J. Zaslavski, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Alexander J. Zaslavski ISBN: 9783319774374
Publisher: Springer International Publishing Publication: May 2, 2018
Imprint: Springer Language: English
Author: Alexander J. Zaslavski
ISBN: 9783319774374
Publisher: Springer International Publishing
Publication: May 2, 2018
Imprint: Springer
Language: English

This book details approximate solutions to common fixed point problems and convex feasibility problems in the presence of perturbations. Convex feasibility problems search for a common point of a finite collection of subsets in a Hilbert space; common fixed point problems pursue a common fixed point of a finite collection of self-mappings in a Hilbert space. A variety of algorithms are considered in this book for solving both types of problems,  the study of which has fueled a rapidly growing area of research. This monograph is timely and highlights the numerous applications to engineering, computed tomography, and radiation therapy planning.

Totaling eight chapters, this book begins with an introduction to foundational material and moves on to examine iterative methods in metric spaces. The dynamic string-averaging methods for common fixed point problems in normed space are analyzed in Chapter 3. Dynamic string methods, for common fixed point problems in a metric space are introduced and discussed in Chapter 4. Chapter 5 is devoted to the convergence of an abstract version of the algorithm which has been called  component-averaged row projections (CARP). Chapter 6 studies a proximal algorithm for finding a common zero of a family of maximal monotone operators. Chapter 7 extends the results of Chapter 6 for a dynamic string-averaging version of the proximal algorithm. In Chapters 8 subgradient projections algorithms for convex feasibility problems are examined for infinite dimensional Hilbert spaces. 

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This book details approximate solutions to common fixed point problems and convex feasibility problems in the presence of perturbations. Convex feasibility problems search for a common point of a finite collection of subsets in a Hilbert space; common fixed point problems pursue a common fixed point of a finite collection of self-mappings in a Hilbert space. A variety of algorithms are considered in this book for solving both types of problems,  the study of which has fueled a rapidly growing area of research. This monograph is timely and highlights the numerous applications to engineering, computed tomography, and radiation therapy planning.

Totaling eight chapters, this book begins with an introduction to foundational material and moves on to examine iterative methods in metric spaces. The dynamic string-averaging methods for common fixed point problems in normed space are analyzed in Chapter 3. Dynamic string methods, for common fixed point problems in a metric space are introduced and discussed in Chapter 4. Chapter 5 is devoted to the convergence of an abstract version of the algorithm which has been called  component-averaged row projections (CARP). Chapter 6 studies a proximal algorithm for finding a common zero of a family of maximal monotone operators. Chapter 7 extends the results of Chapter 6 for a dynamic string-averaging version of the proximal algorithm. In Chapters 8 subgradient projections algorithms for convex feasibility problems are examined for infinite dimensional Hilbert spaces. 

More books from Springer International Publishing

Cover of the book Indigenous Peoples’ Governance of Land and Protected Territories in the Arctic by Alexander J. Zaslavski
Cover of the book Spline and Spline Wavelet Methods with Applications to Signal and Image Processing by Alexander J. Zaslavski
Cover of the book Agroecology by Alexander J. Zaslavski
Cover of the book Advanced Microscopy in Mycology by Alexander J. Zaslavski
Cover of the book Reviews of Environmental Contamination and Toxicology Volume 245 by Alexander J. Zaslavski
Cover of the book Mathematical Concepts by Alexander J. Zaslavski
Cover of the book Biobanking of Human Biospecimens by Alexander J. Zaslavski
Cover of the book The Structural Integrity of Carbon Fiber Composites by Alexander J. Zaslavski
Cover of the book Interactive Storytelling by Alexander J. Zaslavski
Cover of the book Optical Coherence Tomography by Alexander J. Zaslavski
Cover of the book Advances in Endophytic Fungal Research by Alexander J. Zaslavski
Cover of the book Logistics Operations, Supply Chain Management and Sustainability by Alexander J. Zaslavski
Cover of the book High Energy Astrophysical Techniques by Alexander J. Zaslavski
Cover of the book Renewable Energy in the Service of Mankind Vol II by Alexander J. Zaslavski
Cover of the book Globalization and Marginalization in Mountain Regions by Alexander J. Zaslavski
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy