Fast implementation of partial Gram-Schmidt algorithm using tree data structure with sequential row pointers data structure to solve structural problems (PGS)

In this paper, tree data structure with sequential row pointers data structure is developed and used to implement the Partial Gram-Schmidt triangularization algorithm. This algorithm is used to find the solution of linear equations arising from many structural and network problems where the original matrix is non-symmetric and highly sparse, that is, the ratio between zeros and nonzeros elements is very large. An algorithm is developed using the above data structure and results are compared with the method given in M.A. Ajiz, Incomplete Methods For Computer Structural Analysis, PhD Thesis, Queen's University Belfast, 1982 and Ajiz & Jennings, Int. J. Num. Meth. Engng., 20, 949–966, 1984. Conjugate gradients algorithm is used in conjunction with Partial Gram-Schmidt algorithm to obtain the solution of problems obtaining four figure accuracy.