Contents

• Contents
• Introduction
  • The origin of the system
  • Properties from a numerical point of view
• The Sparse QR Factorization
  • The Factorization
  • The Back Substitution
  • Computational costs
• The Optimization
  • Defining the problem
    • Sparsity distance
  • The choice of a search strategy
  • Branch and Bound
    • Branching and Bounding
    • Defining the branch
    • Routine overview
    • Why Heuristics ?
  • The Heuristic
    • Measuring the Quality of Heuristics
• Approaches that failed
  • Using dynamic programming
  • Finding the complete set of possible orderings
• Implementation
  • An overview of the software package
  • Target platforms
  • Choice of languages
  • Implementing Branch and Bound
    • memory handling
• Tools
  • Fortran Code Generation
  • Regression test utility
• Results
  • Sanity testing on sample systems
    • The completely random system
    • The more dense random system
    • The double-diagonal system
    • The upper-triangular system
  • The real system
• Conclusion
• Bibliography

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