Does Matlab use a QR or LU decomposition when solving a matrix equation?

When Matlab computes A\B or A\b does it first compute the LU decomposition of A or the QR decomposition? I'm having accuracy issues and trying to compare my answers to those I get in C using LAPACK.

Thanks very much.

David

Answer 1

[Honglei Chen]

There are actually some information regarding you question in the documentation

http://www.mathworks.com/help/techdoc/ref/mrdivide.html

[David]

Thanks a whole lot. I feel a bit silly that I missed that when I scanned it.

Answer 2

[Paul Metcalf]

I don't know the answer to your question, but you will need to provide more details to get a proper response to your question. For example:

1. Is your matrix A square?
2. What is the size/order of A?
3. When using C/LAPACK, what data types have you cast for A?
4. Are your results only slightly different or dramatically different?

MATLAB using DOUBLE arithmetic for all internal operations. If you are not using real64 types in C, then you might be accumulating quantisation errors...

[David]

1/ The matrix is square, so there's no least-squares solution or anything of that sort

2/ It's order 484

3/ A is double precision in C. On my architecture there's not much gain from single precision and it's not so big that I run into memory issues.

4/ The answers were pretty dramatically different, but it's that the LU decomposition I was using was screwing up. The QR was the right one. Sometimes slower is better!

Looks like the documentation said QR, so that's it. Thanks!

[Paul Metcalf]

Glad you got it sorted. Out of curiosity, how long does your solution take?