CAJ | 학술논문

提出了关于不相容矩阵方程对(AXB, CXD)=(E, F)最小Frobenius范数问题的一个迭代算法.对于任意的初始矩阵X0,在没有舍入误差的情况下,运用此算法能在有限步内得到方程对在Frobenius范数意义下的最小解.数值例子表明所提出算法的有效性.
제출료관우불상용구진방정대(AXB, CXD)=(E, F)최소Frobenius범수문제적일개질대산법.대우임의적초시구진X0,재몰유사입오차적정황하,운용차산법능재유한보내득도방정대재Frobenius범수의의하적최소해.수치례자표명소제출산법적유효성.
This paper presented an iterative algorithm for solving the least Frobenius norm problem of inconsistent matrix equation pair (AXB, CXD)=(E, F) with a real matrix X. By this algorithm, for any (special) initial matrix X0, a solution (the minimal Frobenius norm solution) can be obtained within finite iteration steps in the absence of roundoff errors. The numerical examples verify the efficiency of the algorithm.