Numerical linear algebra algorithms and parallel programming are the essence of grid-like computational systems. Different types of numerical methods based on relevant criteria, such as hybrid, or entropy variants are identified, presented, and implemented as efficient algorithms on parallel computers. This paper reveals the time and complexity of the algorithms, as well as their convergence and shows the usefulness of these concepts for the design of efficient large linear solvers, by illustrating them in dense matrix computations.
One of the aims of this study is the observation of parallel tasks, which are of numerical nature and can arise in many interdisciplinary engineering approaches and consequently in many programming problems, as well as finding and analyzing general algorithms in linear algebra, which are useful in many solutions involving the big data paradigm.
We also demonstrate how to evaluate the worth of such methods, how to prove their competitiveness and how they can be mutated to allow parallel computations, as well as challenging and beating methods used for benchmarking in this aspect.
Algorithm design and analysis, Convergence of numerical methods, Entropy-based heuristic, Dynamic programming, Heuristic algorithms, Hybrid method, Parallel programming