Bi-Periodic Balancing Quaternions

Periodic load balancing

Multiprocessor load balancing aims to improve performance by moving jobs from highly loaded processors to more lightly loaded processors. Some schemes allow only migration of new jobs upon arrival, while other schemes allow migration of jobs in progress. A difficulty with all these schemes, however, is that they require continuously maintaining detailed state information. In this paper we consi...

Nonlinear Parameterization in Bi-Criteria Sample Balancing

Periodic hierarchical load balancing for large supercomputers

Large parallel machines with hundreds of thousands of processors are being built. Ensuring good load balance is critical for scaling certain classes of parallel applications on even thousands of processors. Centralized load balancing algorithms suffer from scalability problems, especially on machines with relatively small amount of memory. Fully distributed load balancing algorithms, on the oth...

Balancing of systems with periodic jumps

In this paper we study the balancing and model-reduction of linear systems with discrete jumps at periodic time instants. These systems arise in the study of linear systems with sampled data control and filtering problems. We study the balancing for the case of fixed and infinite intervals. We show that the system balancing can be used to obtain a reduced order-model of the system with the prop...

Understanding quaternions

The invention of the calculus of quaternions is a step towards the knowledge of quantities related to space which can only be compared for its importance with the invention of triple coordinates by Descartes. The ideas of this calculus, as distinguished from its operations and symbols, are fitted to be of the greatest use in all parts of science.-Clerk Maxwell, 1869. Quaternions came from Hamil...