Hi All, Did Bill's work above for non-constant weight functions get merged into base or a registered package? I'm particularly interested in the Gauss-Hermite quadrature rules. If not, I'll happily use the unregistered package.
Vishal On Tuesday, March 25, 2014 9:54:03 PM UTC-7, Bill McLean wrote: > > Hello Santi Ponte, > > I am not any kind of expert on the QL iteration. All I can suggest is to > check the references listed in the source file src/GaussQuadrature.jl at > lines 65-71 and 303-306. Essentially, I just > rewrote the original Fortran version gaussq.f first into Fortran 90 and > then into Julia. > > Regards, > Bill. > > On Tuesday, March 25, 2014 4:45:50 AM UTC+11, Santi Ponte wrote: >> >> Hallo Bill; could you please explain or post some reference about that >> specialised version you mention of the QL iteration to get directly the >> first components of the normalised eigenvectors. As I am working with >> complex, non-hermitian, symmetric eigenvalue problems it would be of great >> help. Thanks! >> >> El miércoles, 16 de octubre de 2013 03:16:33 UTC+2, Bill McLean escribió: >>> >>> Steven, thanks for pointing out Base.gauss. My package relies, via eig, >>> on the Lapack eigensystem routines for a symmetric tridiagonal matrix, but >>> it would be possible to write such an eigensolver in Julia and so support >>> higher precision. If I find the time I will try to do this. In fact, to >>> generate the Gauss rules you need only the eigenvalues and the first >>> component of each normalized eigenvector, and there is a specialised >>> version of the QL iteration that does this without having to compute the >>> other components of the eigenvectors. >>> >>> On Tuesday, October 15, 2013 6:38:54 AM UTC+11, Steven G. Johnson wrote: >>>> >>>> Note that this functionality (for constant weight functions) is already >>>> in Base, e.g. >>>> >>>> x, w = Base.gauss(Float64, 17) >>>> >>>> gives a 17-point Gauss rule on [-1,1]. There is also Base.kronrod for >>>> Gauss-Kronrod rules. (Currently, these are not documented; that >>>> functionality use used internally by the quadgk function.) >>>> >>>> It is nice to have Gauss quadrature rules for different weight >>>> functions, though. You might want to look at the Base implementation (in >>>> base/quadgk.jl), however, and possibly exploit some of its subroutines, >>>> since the Base implementation supports computation of points and weights >>>> in >>>> arbitrary precision. >>>> >>>> On Saturday, October 12, 2013 9:05:53 PM UTC-4, Bill McLean wrote: >>>>> >>>>> I have written a Julia package to generate the points and weights of >>>>> the classical Gauss quadrature rules. I did not succeed in following the >>>>> instructions in the manual to add it to the list of available packages, >>>>> but >>>>> you can obtain the package from >>>>> https://github.com/billmclean/GaussQuadrature.jl >>>>> >>>>>
