一种采用Householder变换递归实现的复矩阵QR分解算法

QR分解可以改善矩阵条件数,从而提高数值稳定性。由于传统的基于Householder变换的QR分解算法无法有效处理复数矩阵,限制了它的进一步应用。本文提出了一种复数形式的QR分解算法,该算法通过对传统算法进行修改,采用Householder变换递归实现了复矩阵的QR分解,修正后的算法公式可以有效处理复数信号,同时保持了实矩阵QR分解算法的良好性能。新的算法公式对于各种采用QR分解的应用均具有重要意义。通过对其在最小二乘问题中的应用进行仿真,验证了算法在复信号环境下的性能。

A Complex QR Decomposition Algorithm Using Recursive Householder Transformation

QR decomposition can improve the condition number of a matrix and then improve the numerical stability. Because the conventional QR decomposition algorithm based on the Householder transformation cannot handle complex matrix effectively, the application of it is limited. A complex QR decomposition algorithm is proposed. By means of Householder transformation the QR decomposition of a complex matrix can be done recursively. Thereby complex signal data can be processed effectively through this new algorithm while maintaining the performance of its real counterpart. Simulation results in least square problems have demonstrated the validity of the proposed algorithm.