An algebraic technique for total least squares problem in quaternionic quantum theory

被引：11

作者：

Jiang, Tongsong ^{[1
,2
]}

Cheng, Xuehan ^{[3
]}

Ling, Sitao ^{[4
]}

机构：

[1] Linyi Univ, Coll Sci, Linyi 276005, Peoples R China

[2] Here Univ, Dept Math, Heze 274015, Peoples R China

[3] Ludong Univ, Coll Math & Stat Sci, Yantai 264025, Peoples R China

[4] China Univ Min & Technol, Dept Math, State Key Lab Geomech & Deep Underground Engn, Xuzhou 221116, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2016年 / 52卷

基金：

中国国家自然科学基金;

关键词：

Total least squares; Quaternion total least squares; Real representation; Quaternionic quantum theory; MECHANICS;

D O I：

10.1016/j.aml.2015.08.013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The total least squares (TLS) is a method of fitting that is appropriate when there are errors in both the observation vector b = b(mx1) and the data matrix A = A(mxn) In this paper, we study the quaternion total least squares (QTLS) problem by means of real representations of quaternion matrices, and derive an algebraic technique for finding solutions of the QTLS problem in quaternionic quantum theory. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：58 / 63

页数：6

共 12 条

[1]

Adler SL., 1995, QUATERNIONIC QUANTUM

[2] OBSERVABILITY OF QUATERNIONIC QUANTUM-MECHANICS [J].

DAVIES, AJ ;

MCKELLAR, BHJ .

PHYSICAL REVIEW A, 1992, 46 (07) :3671-3675

[3] AN ANALYSIS OF THE TOTAL LEAST-SQUARES PROBLEM [J].

GOLUB, GH ;

VANLOAN, CF .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1980, 17 (06) :883-893

[4]

Golub GH., 2012, MATRIX COMPUTATIONS, V3

[5] Algebraic algorithms for least squares problem in quaternionic quantum theory [J].

Jiang, Tongsong ;

Chen, Li .

COMPUTER PHYSICS COMMUNICATIONS, 2007, 176 (07) :481-485

[6] Algebraic methods for diagonalization of a quaternion matrix in quaternionic quantum theory [J].

Jiang, TS .

JOURNAL OF MATHEMATICAL PHYSICS, 2005, 46 (05)

[7] Equality constrained least squares problem over quaternion field [J].

Jiang, TS ;

Wei, MS .

APPLIED MATHEMATICS LETTERS, 2003, 16 (06) :883-888

[8]

KAISER H, 1984, PHYS REV A, V29, P2276, DOI 10.1103/PhysRevA.29.2276

[9] ANALYSIS OF THE GENERALIZED TOTAL LEAST-SQUARES PROBLEM AX-APPROXIMATE-TO-B WHEN SOME COLUMNS OF A ARE FREE OF ERROR [J].

PAIGE, CC ;

WEI, MS .

NUMERISCHE MATHEMATIK, 1993, 65 (02) :177-202

[10] PROPOSED TEST FOR COMPLEX VERSUS QUATERNION QUANTUM-THEORY [J].

PERES, A .

PHYSICAL REVIEW LETTERS, 1979, 42 (11) :683-686

← 1 2 →