The forward rounding error analysis of the partial pivoting quaternion LU decomposition

In this paper, we consider the forward rounding errors of the partial pivoting quaternion LU decomposition. To carry out error analysis of algorithms in quaternion arithmetic, we first propose the accuracy model for the basic quaternion arithmetic operations by the real structure-preserving method. And then, we study the forward rounding errors of the partial pivoting quaternion LU decomposition. Finally, by using the results of the forward rounding errors of the partial pivoting quaternion LU decomposition, we analyze the forward rounding errors of the nonsingular quaternion linear system.