Performance Analysis of Effective Symbolic Methods for Solving Band Matrix SLAEs
This is an incremental performance comparison of existing symbolic methods for a specific class of linear systems, relevant to researchers using symbolic computation for band matrices.
The paper benchmarks symbolic algorithms for solving band matrix systems, finding that GiNaC-based implementations outperform SymPy-based ones, with speedups of up to 10x on HPC platforms.
This paper presents an experimental performance study of implementations of three symbolic algorithms for solving band matrix systems of linear algebraic equations with heptadiagonal, pentadiagonal, and tridiagonal coefficient matrices. The only assumption on the coefficient matrix in order for the algorithms to be stable is nonsingularity. These algorithms are implemented using the GiNaC library of C++ and the SymPy library of Python, considering five different data storing classes. Performance analysis of the implementations is done using the high-performance computing (HPC) platforms "HybriLIT" and "Avitohol". The experimental setup and the results from the conducted computations on the individual computer systems are presented and discussed. An analysis of the three algorithms is performed.