• 论文 •

### 信号处理中一类非线性方程组的快速求解

1. (1)大连理工大学应用数学系, 大连 116024; (2)吉林大学数学研究所, 长春 130012; (3)哈尔滨工程大学水声工程学院, 哈尔滨 150001.
• 收稿日期:2008-02-13 修回日期:1900-01-01 出版日期:2008-08-25 发布日期:2008-08-25

YU Bo;DONG Bo;CAO Xiaofei;YANG Desen. A Fast Algorithm for a Class of Nonlinear Systems in Signal Processing[J]. Journal of Systems Science and Mathematical Sciences, 2008, 28(8): 1002-1019.

### A Fast Algorithm for a Class of Nonlinear Systems in Signal Processing

YU Bo(1), DONG Bo(1), CAO Xiaofei(2), YANG Desen(3)

1. (1)Department of Mathematics, Dalian University of Technology, Dalian 116024;(2)Department of Mathematics, Jilin University, Changchun 130012; (3)Harbin Engineering University, Harbin 150001.
• Received:2008-02-13 Revised:1900-01-01 Online:2008-08-25 Published:2008-08-25

In signal processing of sonar and radar, we meet a class of nonlinear systems with alterable dimensions, and every equation in the system is a mixed trigonometric polynomial. Because this class of systems have many solutions, and its corresponding least square problems have many local minimal solutions, the classic iteration methods, e.g. Newton's method, can not be applied to find the solutions. On the other hand, if this class of systems is transformed into polynomial systems, and then homotopy methods or symbolic methods is used to solve them, then the solutions can not be found in a short time due to the high complexity. And unfortunately, if the dimension of the problems is very
large, this class of systems even can not be solved by the above methods.
Combining the hybrid methods presented for mixed trigonometric polynomial systems and the coefficient-parameter homotpy keeping the symmetry of the target system, an effective solving method is presented.

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