TWO ALGEBRAIC ALGORITHMS FOR THE LU DECOMPOSITION OF COMMUTATIVE QUATERNION MATRICES AND THEIR APPLICATIONS

The paper proposes two algebraic algorithms for the LU decomposition of com- mutative quaternion matrices. The first of them is an algebraic algorithm based on a complex representation matrix, and the second is a complex structure-preserving algorithm based on Gaussian elimination of commutative quaternion matrices. With their help, it was established that the LU decomposition of commutative quaternion matrices is not unique. The paper also presents the results of numerical implementations of a mathematical model for color image restoration using the proposed algorithms, which demonstrated the higher efficiency of the first algorithm.