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st: Hilbert matrices – Mata testing

Subject   st: Hilbert matrices – Mata testing
Date   Thu, 3 May 2007 20:43:43 +0100

Dear All,

I found in the Mata manual Hilbert matrices. They are defined as a matrix H with
elements H[i,j]=1/(i+j-1). As it says in the help (type help mf_hilbert):
‘Hilbert matrices are notoriously ill conditioned, with near zero

The help also adds ‘Hilbert(n) and invHilbert(n) are used in testing Mata’. I
think that is intuitive as since they are ‘ill matrices’ with very low
determinants and nearly singular you could use them to test the quality of, for
instance, Mata’s solver (e.g., qrsolve, lusolve, qrinv) and different inverters
(e.g., cholinv, invsym).

Am I right?
Could anybody supply an example of how Hilbert matrices are used to test Mata?

Many thanks,


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