8139 Regular Pentagon Dirichlet Eigenvalues (60 digits)
Robert S Jones
rsjones7 at yahoo dot com
April 13, 2015, Finished 60-digit results.
Note, I inadvertently missed one eigenvalue in this calculation. Can you identify it?
I am currently extending these calculations by a factor of 20, so I won't fix it here yet.
The lowest 8139 Dirichlet eigenvalues of the unit-edged, regular pentagon, correctly rounded to sixty digits, are shown on this page. They are divided by symmetry.
This list [hopefully] includes all eigenvalues below 100,000, and the first one above 100,000 (which is in the S-symmetry tower).
- pentagon.DS.nom.dat Non-degenerate Symmetric
- pentagon.DA.nom.dat Non-degenerate Antisymmetric
- pentagon.DB.nom.dat Doubly Degenerate Mixed Modes B
- pentagon.DC.nom.dat Doubly Degenerate Mixed Modes C
Note, to number the lines, I used "$ nl -w 4 pentagon.DS.nom.dat > nl.pentagon.DS.nom.dat". The above files do not have numbered lines.
Dirichlet - S-symmetry (1396 eigenvalues)
Dirichlet - A-symmetry (1318 eigenvalues)
Dirichlet - B-symmetry (2712 eigenvalues)
Dirichlet - C-symmetry (2713 eigenvalues)
- I used the GSVD method to sweep the interval λ∈[0,100002] using an increment of δλ=1. I then carefully looked for nearby eigenvalues (within that δλ). The sweep output is posted here (browser warning, more than 400,000 lines).
- I intend to post the programs and other details as I did for the L-shape.