# Performance Analysis of Effective Symbolic Methods for Solving Band Matrix SLAEs

## TL;DR

This paper evaluates the performance of symbolic algorithms for solving band matrix linear systems using C++ and Python implementations across HPC platforms, highlighting their stability and efficiency.

## Contribution

It provides an experimental performance comparison of three symbolic algorithms implemented with GiNaC and SymPy for band matrix systems on HPC platforms.

## Key findings

- Algorithms are stable for nonsingular matrices.
- Performance varies with data storage classes and platforms.
- Experimental results demonstrate efficiency of symbolic methods.

## Abstract

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.