Heterogeneous Distribution of Computations While Solving Linear Algebra Problems on Networks of Heterogeneous Computers

1 I n t r o d u c t i o n Progress in network technologies is making local and even global networks of computers (in particular, networks of PCs and workstations) more and more attractive for high-performance parallel computing. While developing applications for such networks it is necessary to take into account their heterogeneity being the main peculiarity of common networks differing them from supercomputers. The heterogeneity is displayed at least in two forms. Firstly, in the form of heterogeneity of machine arithmetics of such parallel systems. Related challenges existing in writing reliable numerical library software for heterogeneous computing environments have been analyzed in [1]. Secondly, in the form of heterogeneity of both performances of individual processors and speeds of data transfer between the processors. As a rule, to solve linear algebra problems on a heterogeneous network of computers one uses numeric software originally developed for homogeneous distr ibuted-memory machines and later on ported to the network. As a rule, while computing on such homogeneous computer systems, a strategy of homogeneous distribution of computations over processors is used. The strategy will be referred as the HoBo strategy "Homogeneous distribution of processes over processors Homogeneous distribution of data over the processes", with each physical processor running one process and data being evenly parti t ioned among the processes.