Computational Error and Complexity in Science and Engineering

V. Lakshmikantham and S.K. Sen (Eds.)0444518606, 9780444518606, 9780080459516

The book “Computational Error and Complexity in Science and Engineering” pervades all the science and engineering disciplines where computation occurs. Scientific and engineering computation happens to be the interface between the mathematical model/problem and the real world application. One needs to obtain good quality numerical values for any real-world implementation. Just mathematical quantities symbols are of no use to engineers/technologists. Computational complexity of the numerical method to solve the mathematical model, also computed along with the solution, on the other hand, will tell us how much computation/computational effort has been spent to achieve that quality of result. Anyone who wants the specified physical problem to be solved has every right to know the quality of the solution as well as the resources spent for the solution. The computed error as well as the complexity provide the scientific convincing answer to these questions. Specifically some of the disciplines in which the book will be readily useful are (i) Computational Mathematics, (ii) Applied Mathematics/Computational Engineering, Numerical and Computational Physics, Simulation and Modelling. Operations Research (both deterministic and stochastic), Computing Methodologies, Computer Applications, and Numerical Methods in Engineering. Key Features: – Describes precisely ready-to-use computational error and complexity – Includes simple easy-to-grasp examples wherever necessary. – Presents error and complexity in error-free, parallel, and probabilistic methods. – Discusses deterministic and probabilistic methods with error and complexity. – Points out the scope and limitation of mathematical error-bounds. – Provides a comprehensive up-to-date bibliography after each chapter. · Describes precisely ready-to-use computational error and complexity · Includes simple easy-to-grasp examples wherever necessary. · Presents error and complexity in error-free, parallel, and probabilistic methods. · Discusses deterministic and probabilistic methods with error and complexity. · Points out the scope and limitation of mathematical error-bounds. · Provides a comprehensive up-to-date bibliography after each chapter.

---

Table of contents :
Content:
Preface
Pages v-vi
V. Lakshmikantham, S.K. Sen

Chapter 1 Introduction
Pages 1-24

Chapter 2 Error: Precisely what, why, and how Original Research Article
Pages 25-61

Chapter 3 Complexity: What, why, and how Original Research Article
Pages 63-93

Chapter 4 Errors and approximations in digital computers Original Research Article
Pages 95-145

Chapter 5 Error and complexity in numerical methods Original Research Article
Pages 147-193

Chapter 6 Error and complexity in error-free, parallel, and probabilistic computations Original Research Article
Pages 195-235

Index
Pages 237-248