Matrix iterative algorithms for least-squares problem in quaternionic quantum theory

作     者：Ling, Sitao Jia, Zhigang 

作者机构：China Univ Min & Technol Dept Math Xuzhou 221116 Peoples R China Jiangsu Normal Univ Dept Math Xuzhou 221116 Peoples R China 

出 版 物：《INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS》 (国际计算机数学杂志)

年 卷 期：2013年第90卷第3期

页      面：727-745页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Fundamental Research Funds for the Central Universities [2012QNB22] National Natural Science Foundation of China 

主　　题：quaternion matrix quaternionic least squares LSQR RRLSQR iterative algorithm 65F10 65F30 

摘      要：Quaternionic least squares (QLS) is an efficient method for solving approximate problems in quaternionic quantum theory. Based on Paige s algorithms LSQR and residual-reducing version of LSQR proposed in Paige and Saunders [LSQR: An algorithm for sparse linear equations and sparse least squares, ACM Trans. Math. Softw. 8(1) (1982), pp. 4371], we provide two matrix iterative algorithms for finding solution with the least norm to the QLS problem by making use of structure of real representation matrices. Numerical experiments are presented to illustrate the efficiency of our algorithms.