# [R] System is computationally singular?

Dimitris Rizopoulos dimitris.rizopoulos at med.kuleuven.ac.be
Thu Dec 9 09:27:27 CET 2004

```Hi Rui,

when you are far from the optimum the Hessian might be a non positive
definite matrix and thus it cannot be solved. There are some positive
check at Section 3.2.4 of:

http://www.stat.wisc.edu/~mchung/teaching/stat471/stat_computing.pdf

However, if you have a function computing the minus log-likelihood and
its derivative, then it would be easier to use `optim()', probably
with method "BFGS" (or "CG" if you have many parameters).

I hope it helps.

Best,
Dimitris

----
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven

Tel: +32/16/336899
Fax: +32/16/337015
Web: http://www.med.kuleuven.ac.be/biostat
http://www.student.kuleuven.ac.be/~m0390867/dimitris.htm

----- Original Message -----
From: "Rui Wang" <wangruiwin at hotmail.com>
To: <r-help at stat.math.ethz.ch>
Sent: Thursday, December 09, 2004 4:16 AM
Subject: [R] System is computationally singular?

> Hi all,
>
> I was using the Newton-Raphson method to estimate paremeters in the
> model developed by my supervisor. However, when I interatively
> computed theta(t+1)=theta(t) - solve(H)*s (where the Hessian matrix
> and score vector were explicitely derived), I got the error message:
> Error in solve.default(H) : system is computationally singular:
> reciprocal condition number = 1.70568e-032. Assume my score vector
> and Hessian matrix were correct, could anyone give me some
> suggestion on how to avoid this singular situation? Thank you in
> advance. Maybe this question is not related to R itself, but it is
> kind of statistical computation problems, please forgive me to put
> questions here.
>
> Rui
>
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