Object Oriented Set Theoretic Implementation of Minimum Degree Algorithm

Sparse Symmetric Positive Definite (SPD) Linear System Solvers (LSS) are routinely required in various Power System Analysis problems. In sparse LSS ordering of nodes is desired to reduce fill ins, which in turn reduce computations. Minimum Degree Algorithm (MDA) has established itself as a very competitive ordering algorithm, for reducing fill ins to quite often near minimum level. With the acceptance of Object Oriented (OO) programming for Power System Analysis, there is need to investigate in detail, the OO implementation of numerical linear algebra algorithms. This paper describes an OO based implementation of MDA, for large scale systems, considering enhancements like mass elimination, multiple elimination. Two important characterizations of multiple elimination viz different nodes and similar nodes are discussed. Relevant data structure and efficient implementation within OO framework is developed. is used as the programming language as it is by far the most popular OO programming language.