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Convergence analysis of modulus-based matrix splitting iterative methods for implicit complementarity problems.

An Wang1, Yang Cao2, Quan Shi2

  • 11School of Science, Nantong University, Nantong, 226019 China.

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PubMed
Summary
This summary is machine-generated.

This study presents a complete convergence theory for modulus-based matrix splitting iteration methods. New convergence conditions are established for implicit complementarity problems with positive-definite and [Formula: see text]-matrices.

Keywords:
convergenceimplicit complementarity problemmatrix splittingmodulus-based iterative method

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Area of Science:

  • Numerical Analysis
  • Matrix Theory
  • Computational Mathematics

Background:

  • Implicit complementarity problems present significant challenges in various scientific and engineering fields.
  • Existing iterative methods require further theoretical development for robust convergence analysis.
  • Modulus-based matrix splitting methods offer a promising approach for solving these problems.

Purpose of the Study:

  • To provide a complete convergence theory for modulus-based matrix splitting iteration methods.
  • To extend the applicability of these methods to a broader class of implicit complementarity problems.
  • To establish novel convergence conditions for specific matrix types.

Main Methods:

  • The study builds upon the framework proposed by Hong and Li (2016).
  • It employs rigorous mathematical analysis to derive convergence criteria.
  • The methods are specifically analyzed for systems involving positive-definite matrices and [Formula: see text]-matrices.

Main Results:

  • A comprehensive convergence theory for the modulus-based matrix splitting iteration methods is demonstrated.
  • New and improved convergence conditions are derived.
  • The theoretical results are validated for systems with positive-definite and [Formula: see text]-matrices.

Conclusions:

  • The presented convergence theory enhances the reliability of modulus-based matrix splitting methods.
  • The new conditions expand the scope of solvable implicit complementarity problems.
  • This work contributes to the advancement of numerical linear algebra and computational mathematics.