半正定RICCATI矩阵构造及对合性证明  

Positive Semidefinite RICCATI Matrix Construction and Involution Proof

作　　者：张春生[1] 

机构地区：[1]江西新余学院数学与计算机科学学院,江西新余338000

出　　处：《科技通报》2014年第8期10-12,共3页Bulletin of Science and Technology

摘　　要：半正定对合性RICCATI矩阵在计算机编码和密码通信中具有广阔用途,传统算法中构造RIC.CATI矩阵采用Vandermonde矩阵构造,当矩阵的阶数和较大时,不能直接进行随机搜索,且构造出的RICCATI矩阵具有特定的数学结构,算法实现较为困难。提出采用两个Vandermonde矩阵构造RICCA.TI矩阵,并证明了其充分必要性。利用矩阵标量乘的方法,实现标量乘Vandermonde矩阵构造半正定RICCATI矩阵,证明了矩阵的对合性。该方法构造的半正定对合性RICCATI矩阵可以通过调控标量中分量的大小来调整标量乘矩阵元素大小和元素重量大小,在通信编码等应用领域具有广阔应用前景。The positive semi-definite matrix of RICCATI has wide application in computer codes and communication, and the traditional algorithm for constructing RICCATI matrix established based on Vandermonde matrix. When the order of matrix and large, it cannot directly carry out random search, RICCATI matrix and the mathematical structure is specific, al-gorithm is difficult to realize. The two Vandermonde matrixes is used to construct the RICCATI matrix, and the sufficient and necessary conditions is proved, using the method of matrix scalar multiplication, the scalar multiplication to construct Vandermonde matrix positive semidefinite RICCATI matrix is obtained, research result shows that the matrix of nature. The method to construct the positive semi definite matrix can be adjusted for compliance RICCATI scalar multiplication matrix element size and element size and weight by component control scalar in size, and it has broad application prospect in the application fields such as communication code.

关 键 词：RICCATI矩阵 VANDERMONDE矩阵 对合性 

分 类 号：O241.7[理学—计算数学]