矩阵迹最小问题的求解  

Solving the minimum problem of matrix trace

作　　者：谭婕 彭振赟[1] TAN Jie;PENG Zhenyun(School of Mathematics and Computational Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院

出　　处：《桂林电子科技大学学报》2019年第3期248-253,共6页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11261014);广西自然科学基金(2017GXNFAA198248)

摘　　要：为了探究方程组AXB=C的不定最小二乘问题的解及解的存在条件,利用矩阵相关理论及双曲QR分解理论,给出了一类矩阵迹最小问题有解、有唯一解的充分必要条件和矩阵迹最小问题的解存在时解的计算算法。用数值例子验证该问题有解时计算算法的可行性。In order to explore the solution of the indefinite least squares problem of the system of equations and the existence condition of the solution.Using matrix theory and hyperbolic QR decomposition theory,A necessary and sufficient condition for a class of matrix trace minimization problem to have a solution and a unique solution is given,and a method for calculating the solution of the matrix trace minimization problem is given when the solution exists.Numerical example is used to verify the feasibility of the algorithm when the problem is solved.

关 键 词：矩阵 不定最小二乘问题 矩阵迹最小问题 双曲QR分解 

分 类 号：O241.2[理学—计算数学]