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Spectrum

In: Plane Networks and their Applications

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  • Kai Borre

    (Aalborg University, Danish GPS Center)

Abstract

The spectral density function describes the distribution of eigenvalues of a given problem. Networks may be characterized by the condition number of the normal equation matrix. The spectral condition number is defined as the largest eigenvalue divided by the smallest eigenvalue. Most often this number is several powers of ten. When designing networks the condition number is used as a measure of a good or a bad design. The good design has a low condition number. Therefore it becomes relevant to investigate whether the eigenvalues are dense at the lower and upper part of the spectrum. If they lie dense at both ends, there is little chance to improve the design, while a concentration of eigenvalues at the middle of the spectrum leaves some optimism for achieving a reasonably good design.

Suggested Citation

  • Kai Borre, 2001. "Spectrum," Springer Books, in: Plane Networks and their Applications, chapter 5, pages 127-138, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0165-6_5
    DOI: 10.1007/978-1-4612-0165-6_5
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