Solving the least squares problem using a parallel linear algebra library

One of the important issues in the construction of a parallel Linear Algebra library is the choice of the process structure. The structure that is presented in this article allows for simple functional specifications of the processes and for their compositionality. Each functional specification describes the meaning of the parallel composition of a number of instances of a single process. The communication behaviours of the instances of a process do not occur in its specification. In such a specification, matrices and vectors occur as ordinary mathematical variables. The representations of the matrices and vectors are distributed across the process instances. All library processes conform to the same communication conventions. The library processes can be composed sequentially, without requiring global synchronisation between process calls. As an example, the parallel solution of the least squares problem is discussed.