Optimal real number codes for fault tolerant matrix operations
Zizhong Chen · 2009
It has been demonstrated recently that single fail-stop process failure in ScaLAPACK matrix multiplication can be tolerated without checkpointing. Multiple simultaneous processor failures can be tolerated without checkpointing by encoding matrices using a real-number erasure correcting code. However, the floating-point representation of a real number in today's high performance computer architecture introduces round off errors which can be enlarged and cause the loss of precision of possibly all effective digits during recovery when the number of processors in the system is large.