Numerische Mathematik

, Volume 103, Issue 4, pp 631–642 | Cite as

Efficient Computation of Analytic Bases in Evans Function Analysis of Large Systems

  • Jeffrey Humpherys
  • Björn Sandstede
  • Kevin ZumbrunEmail author
Original article


In Evans function computations of the spectra of asymptotically constant-coefficient linearized operators of large systems, a problem that becomes important is the efficient computation of global analytically varying bases for invariant subspaces of the limiting coefficient matrices. In the case that the invariant subspace is spectrally separated from its complementary invariant subspace, we propose an efficient numerical implementation of a standard projection-based algorithm of Kato, for which the key step is the solution of an associated Sylvester problem. This may be recognized as the analytic cousin of a C k algorithm developed by Dieci and collaborators based on orthogonal projection rather than eigenprojection as in our case. For a one-dimensional subspace, it reduces essentially to an algorithm of Bridges, Derks and Gottwald based on path-finding and continuation methods.


Solitary Wave Invariant Subspace Evans Function Diagonal Block Comput Phys 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Jeffrey Humpherys
    • 1
  • Björn Sandstede
    • 2
  • Kevin Zumbrun
    • 3
    Email author
  1. 1.Brigham Young UniversityProvoUSA
  2. 2.Department of Mathematics and StatisticsUniversity of SurreyGuild-fordUK
  3. 3.Indiana UniversityBloomingtonUSA

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