Re: Options for Eigenvalues

*To*: mathgroup at smc.vnet.net*Subject*: [mg96145] Re: Options for Eigenvalues*From*: Roman <rschmied at gmail.com>*Date*: Sat, 7 Feb 2009 03:49:26 -0500 (EST)*References*: <gmecfo$adp$1@smc.vnet.net>

Sebastian, I'm parsing the error messages of Mathematica 6 here. Maybe there are further undocumented methods and options. The method should be either Automatic or Arnoldi. A call should be formed, for example, like this: Eigenvalues[H, 1, Method -> {Arnoldi, MaxIterations -> 10000, Criteria -> RealPart}] the extra options are: Shift (a complex number) Tolerance (non-negative real number or Automatic) BasisSize (integer >2 and <= matrix size) MaxIterations (integer) StartingVector (a vector of length equal to the matrix size) Criteria: can be Magnitude RealPart ImaginaryPart BothEnds (for real symmetric eigenvalue problems only) To know what these mean, I recommend the ARPACK documentation: http://www.caam.rice.edu/software/ARPACK/ Briefly, the basis size option gives the number of vectors used in the iteration; not even the authors of ARPACK seem to know an optimal choice here. The criteria specify which n eigenvalues are to be computed: those with largest magnitude, largest real part, or largest imaginary part. "BothEnds" computes alternating eigenvalues with small and large real parts. "Shift" is for shifting the spectrum around (shift-invert method) to pick out eigenvalues from the center of the spectrum, close to a previously known value. hth Roman.