Parallel Solvers for Sylvester-Type Matrix Equations with Applications in Condition Estimation, Part II: The SCASY Software Library

We continue our presentation of parallel ScaLAPACK-style algorithms for solving Sylvester-type matrix equations. In Part II, we present SCASY, a state-of-the-art HPC software library for solving 44 sign and transpose variants of eight common standard and generalized Sylvester-type matrix equations. The internal design of the library, Fortran interfaces and implementation issues are discussed in some detail. In addition, experimental results from a distributed memory platform with NUMA nodes illustrates the performance of SCASY when linked with the OpenMP version of the node solver library RECSY and a threaded BLAS implementation. This demonstrates SCASY’s novel capacity and functionality in being able to concurrently handle both the message passing model and the multiple threading model for parallel computing.