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A Method To Solve Multivariate Polynomial Systems In Max Algebra Using Extended Linear Complementarity.pdf

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Preview of A Method to Solve Multivariate Polynomial Systems in Max Algebra using Extended Linear Complementarity
🔗 Source: dcsc.tudelft.nl
📊 Size: 399 KB
📄 Pages: 25 pages
⬇️ Downloads: 216

Summary

A Method to Find Solutions of Multivariate Polynomial Equations and Inequalities in Max Algebra

This technical report (K.U. Leuven, ESAT) by B. De Schutter and B. De Moor presents a method to solve systems of multivariate polynomial equalities and inequalities within the framework of max algebra.

Key Insights:

Equivalence to Extended Linear Complementarity Problem (ELCP): The authors demonstrate that finding solutions in max algebra reduces to solving an ELCP, a fundamental problem in mathematical programming.
 Algorithmic Solution: They provide an algorithm to solve the ELCP, which directly leads to all solutions of the original multivariate polynomial system.
Geometrical Insight: The approach offers a geometric understanding of solution sets within the max algebra.
 Broader Applications: The method extends to various problems in max algebra and max-min-plus algebra, including:
Matrix decompositions
 State space transformations
Construction of matrices with specific characteristic polynomials
 Minimal state space realization

Methodology:

1. ELCP Formulation: The report defines an ELCP, extending the traditional Linear Complementarity Problem to handle max-algebraic operations (max and addition).
2. Algorithm: It outlines a procedure to solve the ELCP, utilizing its equivalence to the multivariate polynomial system.
3. Solution Set Analysis: The solution set in max algebra is analyzed geometrically, providing insights into the structure of solutions.

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Description

This technical report from KU Leuven's Department of Electrical Engineering presents a method to solve systems of multivariate polynomial equalities and inequalities using max algebra, published in Discrete Event Dynamic Systems in 1996. The authors provide an online preprint and reference for further citation.

Technical Information

  • File Format: PDF
  • File Size: 399 KB
  • Pages: 25
  • Language: EN
  • Total Downloads: 216
  • Last Updated: 2 weeks ago

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This PDF document about A Method to Solve Multivariate Polynomial Systems in Max Algebra using Extended Linear Complementarity provides comprehensive information and guidance. Whether you're a beginner or advanced user, this resource offers valuable insights into A Method to Solve Multivariate Polynomial Systems in Max Algebra using Extended Linear Complementarity.

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Method guideMethod tutorialSolve guideSolve tutorialMultivariate guideMultivariate tutorialPolynomial guidePolynomial tutorialSystems guideSystems tutorialAlgebra guideAlgebra tutorialusing guideusing tutorialExtended guideExtended tutorialLinear guideLinear tutorialComplementarity guideComplementarity tutorial

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