A Study on the Efficient m-step Parallel Generalization

It would be desirable to have methods for specific problems, which have low communication costs compared to the computation costs, and in specific applications, algorithms need to be developed and mapped onto parallel computer architectures. Main memory access for shared memory system or global communication in message passing system deteriorate the computation speed. In this paper, it is found that the m-step generalization of the block Lanczos method enhances parallel properties by forming m simultaneous search direction vector blocks. QR factorization, which lowers the speed on parallel computers, is not necessary in the m-step block Lanczos method. The m-step method has the minimized synchronization points, which resulted in the minimized global communications compared to the standard methods.