. "0450] where A is an N???N matrix of coefficients, b is an N???1 column vector, and x is the N???1 solution being sought. [0451] To solve for x, an LU factorization is performed on A. LU factorization results in a lower triangular matrix L and upper triangular matrix U such that A=L???U. Substituting forA in the original equation, LUx=b or Ux=L???1b, and x may also be solved. [0452] First, A and b" . . .