## ABSTRACT

In this chapter, we focus on the graph-grammar production responsible for partial LU factoriza-

tion in the general case, where we have a matrix A with n rows fully assembled, and m not fully assembled rows, thus the total size of the matrix is m + n. In such a case we deal with

the following system of linear equations The example interface code can be downloaded from

://www.ki.agh.edu.pl/FastSolvers/Chapter7

A(1,1) x(1)+A(1,2) x(2) = b(1) A(2,1) x(1)+A(2,2)x(2) = b(2)

where A(1,1) is a square matrix of size n × n, A(1,2) is a matrix of size n × m, A(2,1) is a matrix of size m × n, A(2,2) is a matrix of size m ×m. Additionally, the right-hand side b(1) is a vector of size n and b(2) is a vector of size m.