The first part takes , the second part takes , and the third takes . For constant values of P and Q , is a constant. Thus, is directly proportional to X . We define the checkpointing rate R to be the rate of sending a message and performing addition on the message, measured in bytes per second. The first part takes time, and the second takes time.
Hessenberg reduction is an operation for solving an nonsymmetric eigenvalue problem.
Note that we choose the right-looking algorithms for the factorizations. In our implementations, we added to the matrix operations one-dimensional parity in such a way that one checkpointing processor is dedicated to checkpoint a column of processors. This network consists of 24 workstations, each with 96 Mbytes of RAM, connected by a switched 100 megabit Ethernet. The peak measured bandwidth in this configuration is 40 megabits per second between two random workstations. We ran our experiments on these machines when we could allocate them exclusively for our own use.