Computational Error and Complexity in Science and Engineering - 1st Edition - ISBN: 9780444518606, 9780080459516

Computational Error and Complexity in Science and Engineering, Volume 201

1st Edition

Computational Error and Complexity

Authors: Vangipuram Lakshmikantham Syamal Sen
Hardcover ISBN: 9780444518606
eBook ISBN: 9780080459516
Imprint: Elsevier Science
Published Date: 4th March 2005
Page Count: 260
Tax/VAT will be calculated at check-out
195.00
120.00
149.00
175.00
Unavailable
Compatible Not compatible
VitalSource PC, Mac, iPhone & iPad Amazon Kindle eReader
ePub & PDF Apple & PC desktop. Mobile devices (Apple & Android) Amazon Kindle eReader
Mobi Amazon Kindle eReader Anything else

Institutional Access


Table of Contents

  • Preface
  • Chapter 1: Introduction
    • 1.1 Science versus engineering
    • 1.2 Capability and limit of computation
    • 1.3 What is computation in science and engineering
    • 1.4 Tools for Computation
    • 1.5 Algorithms and Complexity
    • 1.6 Types of computation
    • 1.7 Models of computation
    • 1.8 Computer representable numbers: Scope and error
    • 1.9 Problem-solving: Stages and error
    • 1.10 Stages of problem-solving: Equivalence and hierarchical structure
  • Chapter 2: Error: Precisely What, Why, and How
    • 2.1 Introduction
    • 2.2 Error: Precisely what and how to compute
    • 2.3 Error-free environment/quantity — How far is it possible
    • 2.4 Error analysis
    • 2.5 Limitation of interval arithmetic and significant digit arithmetic
    • 2.6 Visualization of error
    • 2.7 Mathematical error versus computable error
    • 2.8 Confidence versus error
    • 2.9 Error-bound is non-decreasing while actual error need not be
    • 2.10 Stability and error
  • Chapter 3: Complexity: What, Why, and How
    • 3.1 Introduction
    • 3.2 Algorithm as Turing machine and algorithmic complexity
    • 3.3 Pspace
    • 3.4 Alternation
    • 3.5 Logspace
    • 3.6 Probabilistic complexity
    • 3.7 Descriptive complexity
    • 3.8 Boolean circuit complexity
    • 3.9 Communication complexity
    • 3.10 Quantum complexity
    • 3.11 Parallel complexity
  • Chapter 4: Errors and Approximations in Digital Computers
    • 4.1 Introduction
    • 4.2 Number representation
    • 4.3 Fixed- and floating-point representation and a arithmetic
    • 4.4 Error in function with approximate arguments (direct problem)
    • 4.5 Error in arguments with prescribed accuracy in function (inverse problem)
    • 4.6 Significance of a function
    • 4.7 Error in series approximation
    • 4.8 Base 2 system: best in computer/communication
    • 4.9 IEEE 754 floating-point format
  • Chapter 5: Error and Complexity in Numerical Methods
    • 5.1 Introduction
    • 5.2 Error in quantities and computations
    • 5.3 Computational complexity
    • 5.4 What computer can represent
    • 5.5 Algorithms and related errors
    • 5.6 Conclusions
  • Chapter 6: Error and Complexity in Error-Free, Parallel, and Probabilistic Computations
    • 6.1 Introduction
    • 6.2 Actual error-bound in exact computation: Exponential problem
    • 6.3 Parallel computation: error and complexity
    • 6.4 Error-bounds in probabilistic computation
    • 6.5 Shrinking-rectangle randomized algorithm for complex zero: Error and complexity
  • Index

Description

  • Preface
  • Chapter 1: Introduction
    • 1.1 Science versus engineering
    • 1.2 Capability and limit of computation
    • 1.3 What is computation in science and engineering
    • 1.4 Tools for Computation
    • 1.5 Algorithms and Complexity
    • 1.6 Types of computation
    • 1.7 Models of computation
    • 1.8 Computer representable numbers: Scope and error
    • 1.9 Problem-solving: Stages and error
    • 1.10 Stages of problem-solving: Equivalence and hierarchical structure
  • Chapter 2: Error: Precisely What, Why, and How
    • 2.1 Introduction
    • 2.2 Error: Precisely what and how to compute
    • 2.3 Error-free environment/quantity — How far is it possible
    • 2.4 Error analysis
    • 2.5 Limitation of interval arithmetic and significant digit arithmetic
    • 2.6 Visualization of error
    • 2.7 Mathematical error versus computable error
    • 2.8 Confidence versus error
    • 2.9 Error-bound is non-decreasing while actual error need not be
    • 2.10 Stability and error
  • Chapter 3: Complexity: What, Why, and How
    • 3.1 Introduction
    • 3.2 Algorithm as Turing machine and algorithmic complexity
    • 3.3 Pspace
    • 3.4 Alternation
    • 3.5 Logspace
    • 3.6 Probabilistic complexity
    • 3.7 Descriptive complexity
    • 3.8 Boolean circuit complexity
    • 3.9 Communication complexity
    • 3.10 Quantum complexity
    • 3.11 Parallel complexity
  • Chapter 4: Errors and Approximations in Digital Computers
    • 4.1 Introduction
    • 4.2 Number representation
    • 4.3 Fixed- and floating-point representation and a arithmetic
    • 4.4 Error in function with approximate arguments (direct problem)
    • 4.5 Error in arguments with prescribed accuracy in function (inverse problem)
    • 4.6 Significance of a function
    • 4.7 Error in series approximation
    • 4.8 Base 2 system: best in computer/communication
    • 4.9 IEEE 754 floating-point format
  • Chapter 5: Error and Complexity in Numerical Methods
    • 5.1 Introduction
    • 5.2 Error in quantities and computations
    • 5.3 Computational complexity
    • 5.4 What computer can represent
    • 5.5 Algorithms and related errors
    • 5.6 Conclusions
  • Chapter 6: Error and Complexity in Error-Free, Parallel, and Probabilistic Computations
    • 6.1 Introduction
    • 6.2 Actual error-bound in exact computation: Exponential problem
    • 6.3 Parallel computation: error and complexity
    • 6.4 Error-bounds in probabilistic computation
    • 6.5 Shrinking-rectangle randomized algorithm for complex zero: Error and complexity
  • Index

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.

Readership

Students of Computational/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. Evolutionary Computation, Genetic Algorithms/Programming.


Details

No. of pages:
260
Language:
English
Copyright:
© Elsevier Science 2005
Published:
Imprint:
Elsevier Science
eBook ISBN:
9780080459516
Hardcover ISBN:
9780444518606

About the Authors

Vangipuram Lakshmikantham Author

Affiliations and Expertise

Florida Institute of Technology, Melbourne, FL, USA

Syamal Sen Author

Affiliations and Expertise

Florida Institute of Technology, Melbourne, FL, USA