You may want to look at the following paper.

Best,

Giovanni

Reference Type: Journal Article

Author: Pinheiro, JosÃ© C.

Author: Bates, Douglas M.

Primary Title: Unconstrained parametrizations for variance-covariance

matrices

Journal Name: Statistics and Computing

Cover Date: 1996-09-01

Publisher: Springer Netherlands

Issn: 0960-3174

Subject: Computer Science

Start Page: 289

End Page: 296

Volume: 6

Issue: 3

Url:

http://dx.doi.org/10.1007/BF00140873Doi: 10.1007/BF00140873

On Fri, 2011-11-18 at 06:07 -0800, Pacin Al wrote:

> Hi,

>

> I would like to know what should I garantee about P and GGt in order to have

>

> F = Z %*% P %*% t(Z) + GGt always as a positive definite matrix.

>

> Being more precise:

>

> I am trying to find minimum likelihood parameters by using the function

> 'optim' to find the lowest value generated by $LogLik from the function

> 'fkf' (

http://127.0.0.1:27262/library/FKF/html/fkf.html).

>

> The variable Kt within the algorithm used to generate the Kalman Filter

> equations needs in each iteration the inverse of the variable Ft, ("Kt[,, i]

> = Pt[,, i] %*% t(Zt[,, i]) %*% solve(Ft[,, i])") which is updated by "Ft[,,

> i] = Zt[,, i] %*% Pt[,, i] %*% t(Zt[,, i]) + GGt[,, i]".

>

> Zt is a constant 2x4 matrix and can't be changed. Gt (2x2) and P0 (4x4) are

> inputs for 'fkf'. Pt is updated in each iteration, starting with P0. GGt is

> constant and one of the parameters tested by 'optim' to minimize the LogLik

> (by the way, GGt is always positive definite). Except for the first

> parameters that I give to 'optim', I can't control its tested parameters,

> which will be used as the inputs of 'fkf' (except, as I sad, for Gt, because

> I ask 'optim' to give GLt, the lower triangular matrix of Gt, giving as

> input to 'fkf' GLt %*% t(GLt) ).

>

> Since the process stops every time a non positive matrix Ft appears, I would

> like to know if are there any transformations that could be applied to GGt

> and P0, given by 'optim', to be sure that Ft will be always positive

> definite.

>

>

>

>

>

>

> --

> View this message in context:

http://r.789695.n4.nabble.com/Ensuring-a-matrix-to-be-positive-definite-case-involving-three-matrices-tp4083376p4083376.html> Sent from the R help mailing list archive at Nabble.com.

>

> ______________________________________________

>

[hidden email] mailing list

>

https://stat.ethz.ch/mailman/listinfo/r-help> PLEASE do read the posting guide

http://www.R-project.org/posting-guide.html> and provide commented, minimal, self-contained, reproducible code.

--

Giovanni Petris <

[hidden email]>

Associate Professor

Department of Mathematical Sciences

University of Arkansas - Fayetteville, AR 72701

Ph: (479) 575-6324, 575-8630 (fax)

http://definetti.uark.edu/~gpetris/______________________________________________

[hidden email] mailing list

https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide

http://www.R-project.org/posting-guide.htmland provide commented, minimal, self-contained, reproducible code.