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Advances in the Efficiency of Computational Methods and Applications cover

This invaluable textbook creates a general framework for the study of optimal iterative procedures for problems that are solved approximately. Emphasis is given to the efficiency of numerical methods. For generality the setting is abstract, but the book presents many applications to practical problems, allowing the reader to take advantage of the most modern high speed calculating devices, and provides examples to illustrate concepts and major theorems. The examples are selected from astrophysics (radiative transfer and the kinetic theory of gases), mechanics (elasticity), economics (predator–prey problems), the n-dimensional Euclidean space and other applied areas. At the end of the textbook, contemporary numerical algorithms to be used for high speed computations have been included.

The book will benefit not only senior undergraduates, graduate students and researchers in the field but also those who wish to obtain information about specific results or techniques that take into account the particular nature of the equation.

Sample Chapter(s)
Chapter 1: Divided Differences (855 KB)

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Contents:
  • Divided Differences
  • Constants and Functions Appearing in Numerical Methods
  • Convergence and Error Analysis for Iterative Methods
  • Special Topics
  • Convergence in Generalized Banach Spaces
  • Discretization of Newton-like Methods
  • Convergence Analysis Based on the Second Fréchet Derivative
  • Forcing Sequences and the Second Fréchet-Derivative
  • Numerical Algorithms

Readership: Senior undergraduates, graduate students and researchers in computational mathematics.

Free Access
FRONT MATTER
  • Pages:i–xi

https://doi.org/10.1142/9789812792709_fmatter

No Access
Divided Differences
  • Pages:1–27

https://doi.org/10.1142/9789812792709_0001

No Access
Constants and Functions Appearing in Numerical Methods
  • Pages:29–55

https://doi.org/10.1142/9789812792709_0002

No Access
Convergence and Error Analysis for Iterative Methods
  • Pages:57–153

https://doi.org/10.1142/9789812792709_0003

No Access
Special Topics
  • Pages:155–206

https://doi.org/10.1142/9789812792709_0004

No Access
Convergence in Generalized Banach Spaces
  • Pages:207–245

https://doi.org/10.1142/9789812792709_0005

No Access
Discretization of Newton-Like Methods
  • Pages:247–322

https://doi.org/10.1142/9789812792709_0006

No Access
Convergence Analysis Based on the Second Fréchet-Derivative
  • Pages:323–417

https://doi.org/10.1142/9789812792709_0007

No Access
Forcing Sequences and the Second Fréchet-Derivative
  • Pages:419–501

https://doi.org/10.1142/9789812792709_0008

Free Access
BACK MATTER
  • Pages:503–546

https://doi.org/10.1142/9789812792709_bmatter

“The book is well-written and accessible to people with a good background in calculus and functional analysis. It can be recommended as a reference work for researchers with an interest in the solution of nonlinear problems. It would also be suitable for an advanced numerical analysis course.”
Mathematics Abstracts

“This book is extremely valuable for graduate students, for scientists, and for specialists.”
Mathematical Reviews