Search

Abstract: In this paper, we discuss the Cholesky decomposition of the Hermitian positive definite quaternion matrix. For the first time, the structure-preserving Gauss transformation is defined, and then a novel structure-preserving algorithm, which is applied to its real representation matrix, is proposed. Our algorithm needs only real number operations, does not depend on the quaternion toolbox for matlab (QTFM) and has more portability. Although the flops of our algorithm are theoretically about the same as those based on quaternion arithmetic operations or QTFM, numerical experiments show that our algorithm runs faster. [Copyright &y& Elsevier]

Abstract: In this paper, we propose two iterative algorithms to solve the matrix equation AXB + CX T D = E. The first algorithm is applied when the matrix equation is consistent. In this case, for any (special) initial matrix X 1, a solution (the minimal Frobenius norm solution) can be obtained within finite iteration steps in the absence of roundoff errors. The second algorithm is applied when the matrix equation is inconsistent. In this case, for any (special) initial matrix X 1, a least squares solution (the minimal Frobenius norm least squares solution) can be obtained within finite iteration steps in the absence of roundoff errors. Some examples verify the efficiency of these algorithms. [Copyright &y& Elsevier]