Chapter 4. Interval Methods for Non-Linear Equation Solving Applications

  1. Dr. Witold Pedrycz MSc, PhD, DSci professor Research Chair member editor-in-chief associate editor recipient2,3,
  2. Andrzej Skowron PhD, DSci Professor Full Professor supervisor editor-in-chief member coeditor-in-chief president program committee member program chair Honorary Professor4 and
  3. Dr. Vladik Kreinovich MSc, PhD visiting scholar invited professor member comaintainer foreign member recipient corecipient5
  1. Courtney Ryan Gwaltney BSc, PhD,
  2. Youdong Lin BS, MS, PhD research associate,
  3. Luke David Simoni BS, PhD Presidential Fellowship and
  4. Mark Allen Stadtherr BChE, PhD professor

Published Online: 16 JUL 2008

DOI: 10.1002/9780470724163.ch4

Handbook of Granular Computing

Handbook of Granular Computing

How to Cite

Gwaltney, C. R., Lin, Y., Simoni, L. D. and Stadtherr, M. A. (2008) Interval Methods for Non-Linear Equation Solving Applications, in Handbook of Granular Computing (eds W. Pedrycz, A. Skowron and V. Kreinovich), John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470724163.ch4

Editor Information

  1. 2

    University of Alberta, Canada

  2. 3

    Polish Academy of Sciences, Warsaw, Poland

  3. 4

    Warsaw University, Poland

  4. 5

    University of Texas, USA

Author Information

  1. University of Notre Dame, Australia

Publication History

  1. Published Online: 16 JUL 2008
  2. Published Print: 18 JUL 2008

ISBN Information

Print ISBN: 9780470035542

Online ISBN: 9780470724163



  • interval arithmetic and real arithmetic extension;
  • containment sets (csets) and interval arithmetic models;
  • non-linear equation key concepts - contraction operators or contractors;
  • Krawczyk and interval-Newton methods;
  • liquid–liquid phase equilibrium modeling;
  • interval methods and non-linear equation application;
  • transition-state analysis;
  • ecological models - food web models;
  • interval-Newton method and non-linear equation systems


This chapter contains sections titled:

  • Overview

  • Background

  • Modeling of Liquid–Liquid Phase Equilibrium

  • Transition-State Analysis

  • Food Web Models

  • Concluding Remarks

  • Acknowledgments

  • References