### Question on a matrix with a particular structure

Posted:

**Fri Jan 07, 2005 4:47 am**Dear LAPACK Forum

We have just implemented LAPACK into our software for solving our matrices and it has speed up our processing from 3 hours to 50minutes! I would really like to thank you for that! This will save us a lot of CPU time and also wait time. I only wish I had found out about this many many years ago!!!

Besides these thanks I would also like to take this opportunity for a small question. I need to invert (or at least solve) a symmetrical positive definite matrix A of the following form:

where:

- a11 is a square (n by n) full (more or less) matrix, and

- a22 is square (m by m, m<n) (band) diagonal matrix, and

- a12 (and its transposed a21) is a (more or less) full matrix.

Is there any particular routine/driver in LAPACK to invert this matrix

more smartly than with the DPOTRx routines which I am using right now!? My Linear Algebra classes are a bit long in the past to remember the details which makes it difficult to understand (parts of) the documentation. I have been and am reading the user guide but did not find something applicable for this. Can you help out a bit!?

Many thanks in advance,

Tim

We have just implemented LAPACK into our software for solving our matrices and it has speed up our processing from 3 hours to 50minutes! I would really like to thank you for that! This will save us a lot of CPU time and also wait time. I only wish I had found out about this many many years ago!!!

Besides these thanks I would also like to take this opportunity for a small question. I need to invert (or at least solve) a symmetrical positive definite matrix A of the following form:

- Code: Select all
`A = ( a11 a12 )`

( a21 a22 )

where:

- a11 is a square (n by n) full (more or less) matrix, and

- a22 is square (m by m, m<n) (band) diagonal matrix, and

- a12 (and its transposed a21) is a (more or less) full matrix.

Is there any particular routine/driver in LAPACK to invert this matrix

more smartly than with the DPOTRx routines which I am using right now!? My Linear Algebra classes are a bit long in the past to remember the details which makes it difficult to understand (parts of) the documentation. I have been and am reading the user guide but did not find something applicable for this. Can you help out a bit!?

Many thanks in advance,

Tim