Algorithmic Cholesky factorization fault recovery

Modeling and analysis of large scale scientific systems often use linear least squares regression, frequently employing Cholesky factorization to solve the resulting set of linear equations. With large matrices, this often will be performed in high performance clusters containing many processors. Assuming a constant failure rate per processor, the probability of a failure occurring during the execution increases linearly with additional processors. Fault tolerant methods attempt to reduce the expected execution time by allowing recovery from failure. This paper presents an analysis and implementation of a fault tolerant Cholesky factorization algorithm that does not require checkpointing for recovery from fail-stop failures. Rather, this algorithm uses redundant data added in an additional set of processors. This differs from previous works with algorithmic methods as it addresses fail-stop failures rather than fail-continue cases. The implementation and experimentation using ScaLAPACK demonstrates that this method has decreasing overhead in relation to overall runtime as the matrix size increases, and thus shows promise to reduce the expected runtime for Cholesky factorizations on very large matrices.