I’m doing an assignment of linear algebra, to compare the performance and stability of QR factorization algorithms Gram-Schmidt and Householder.
My doubt comes when calculating the following table:
Where the matrices Q and R are the resulting matrices of the QR factorizations by applying the Gram-Schmidt and householder to a Hilbert matrix A, I is the identity matrix of dimension N; and || * || is the Frobenius norm.
When I do the calculations on different computers i have different results in some cases, may be due to this?. The above table corresponds to the calculations performed in a 32-bit computer and the next table in a 64-bit:
These results in matlab involves computer architectures in which the calculations were made?
That depends on matlab implementation. Do you get the same result when rerun on same architecture? If yes, this problem may caused by precision. Sometimes, it is caused by different FPU (floatingpoint process uint) of CPU. You may try on more 32-bit/64-bit with different CPU.
The best answer should be reply by your matlab provider. Just call them if you have valid license.
According this link.
one cause of difference is that if calculations are done on with the x87 instructions, it get held in 80 bit precision. depending on compiler optimisations, it numbers may stay at 80bit for a few operation before being truncated back to 64 bit. this can cause variations. see http://gcc.gnu.org/wiki/x87note for more info.
the gcc man pages says that using sse (instead of 387) is default on x86-64 platforms. you should be able to force it on 32bit using something like
-mfpmath=sse -msse -msse2