Timings on Cholesky

It is quite amazing how fast these three alternatives for Cholesky are. Here is a model to time the performance and accuracy. Some results are listed below.

Method	Time	Accuracy	Time	Accuracy	Time	Accuracy
	n=50		n=100		n=200
Nonlinear Equations	0.148	9.6e-8	0.917	1.2e-4	8.991	0.621
External Solver	0.024	1.6e-13	0.025	1.9e-10	0.056	1.4e-5
GAMS Algorithm	0.034	1.9e-13	0.482	6.3e-11	7.571	7.7e-6

I am surprised that the GAMS algorithm is competitive. Notice the accuracy issues when using nonlinear equations due to ill-conditioning of the system of non-linear equations (small changes in a(i,j) lead to large changes in L(i,j)).

Here is some info about the external solver:

c:\>cholesky
CHOLESKY: matrix decomposition A=LL^T
Usage
   > cholesky gdxin i a gdxout L
where
   gdxin  : name of gdxfile with matrix
   i      : name of set used in matrix
   a      : name of 2 dimensional parameter inside gdxin
   gdxout : name of gdxfile for results (factor L)
   L      : name of 2 dimensional parameter inside gdxout
 
Calculates the Cholesky decomposition A=LL^T of a symmetric
positive definite matrix A=a(i,j) where i and j are aliased sets.
L will contain the Cholesky factor L(i,j)
 
 
C:\>