Parallel Polynomial and Matrix Computations

Summary

In this chapter we will survey the techniques of the design of algorithms that effectively solve the computational problems of the previous chapters on parallel computers, reaching a substantial (and frequently dramatic) acceleration of the known sequential algorithms. In some cases this requires us to revise the sequential case approach or even to change it completely. We systematically review the state of the art in this area, in particular, the computational complexity estimates, the algorithms supporting them, and the major techniques for the design of effective parallel algorithms. We include several recent research results and techniques, particularly in sections 4 and 6 and in the appendices. The results of Appendices B and C on computing a maximal independent subset of a vector set and the techniques of the design of parallel algorithms demonstrated in Appendix A may be of interest for the designers of combinatorial and graph algorithms.