| 两类矩阵方程的极小范数最小二乘三对角Hermite解 |
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| 引用本文： | 冯艳昭,张澜.两类矩阵方程的极小范数最小二乘三对角Hermite解[J].高等学校计算数学学报,2020(2):106-119. |
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| 作者姓名： | 冯艳昭 张澜 |
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| 作者单位： | 内蒙古工业大学理学院 |
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| 摘 要： | 1引言矩阵方程广泛应用于诸多领域,例如:控制理论1],系统稳定性分析2]等.对矩阵方程的研究虽然已取得一系列重要成果3-9],但仍然是数值代数领域中热门的课题之一.此外,由于三对角矩阵在诸多学科领域中的广泛应用,使得三对角矩阵倍受人们的关注.文献10]利用Moore-Penrose广义逆及Kronecker积,给出四元数矩阵方程AXB=C的三对角Hermite极小范数最小二乘解和三对角双Hermite极小范数最小二乘解。
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| 关 键 词： | Kronecker积 极小范数最小二乘解 三对角矩阵 矩阵方程 数值代数 HERMITE解 最小二乘 |
MINIMAL NORM LEAST SQUARES TRIDIAGONAL HERMITE SOLUTIONS FOR TWO TYPES OF MATRIX EQUATIONS |
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| Feng Yanzhao,Zhang Lan.MINIMAL NORM LEAST SQUARES TRIDIAGONAL HERMITE SOLUTIONS FOR TWO TYPES OF MATRIX EQUATIONS[J].Numerical Mathematics A Journal of Chinese Universities,2020(2):106-119. |
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| Authors: | Feng Yanzhao Zhang Lan |
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| Institution: | (Science of College,Inner Mongolia University of Technology,Hohhot 010051) |
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| Abstract: | Using Moore-Penrose generalized inverse,Kronecker product and matrix straightening theory,the complex matrix equation is transformed into a real matrix equation.Based on the structural characteristics of tridiagonal Hermite matrix,the least squares tridiagonal Hermite solutions of two types of matrix equations are given,and the numerical algorithm and corresponding examples are given to illustrate the correctness and effectiveness of the theory. |
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| Keywords: | Complex matrix equation Moore-Penrose generalized inverse Kronecker product Matrix straighten Tridiagonal Hermite solution |
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