2024S326295: Matrix Dimention

Good Day!

I'm attempting to tackle the assignment. The algorithm I've written can handle equations with 'n' up to 1000 for a randomly generated matrix, but as the dimension increases, there's a higher chance of encountering a zero denominator. I believe normalization becomes essential in such scenarios. I'm curious about the maximum dimension we should consider for the matrix. [For a matrix with 1000 rows takes around 370ms to solve the equation sequentially]

Please let me know if I am in the right spot.

Kind Regards,

Ehsan

Re: Matrix Dimention

par Wolfgang Schreiner, dimanche 14 avril 2024, 16:32

The assignment has to be performed for dimensions n in the range of several thousands to show decent speedups.
If you encounter a pivot 0, you have to swap the corresponding row with another value that has a non-zero value in that position. If you encounter a matrix that has not full rank (i.e., all not yet processed rows have 0 in the pivot position), abort and choose another one for benchmarking (however, for large dimension n and field size p, the probability to encounter such a matrix is very low).