High-Performance Computation of the Exponential of a Large Sparse Matrix

Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling squaring algorithm (SSA) is not suitable for computation it requires greater memories computational cost than actually needed. By introducing two novel concepts, i.e., real bandwidth bandwidth, to measure sparsity matrix, analyzed. It found that every computed phase SSA, a corresponding approximate exists. To obtain new filtering technique terms forward error analysis proposed. Combining with idea keeping track incremental part, competitive developed exponential. proposed method can primarily alleviate over-scaling problem due technique. Three sets numerical experiments, including one dimension larger 2e6 , are conducted. experiments show that, compared expm function MATLAB, provide higher accuracy at lower less memory.