Why Are We Still Doing This?
Many mathematical modeling problems reduce to this problem
Good libraries available
- LAPACK, ScaLAPACK, PETSc, NAG, IMSL, …
Why is it still hard after all these years?
- Problems get bigger
- FE modeling: 39M unknowns
- Satellite dataset (dense sym eigenvalue problem): 1M unknowns
- RISC based parallel machines harder to program efficiently
- Moving one word of data between processors cost up to O(1000) arithmetic operations
- Effectively using 10’s of thousands of processes can be difficult.
- Accuracy requirement higher
- Find a few correct digits of an eigenvalue
- ~ 10-70, without using > 70 digit arithmetic
Need new algorithms and software implementations