Algebraic algorithms for least squares problem in quaternionic quantum theory

Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations A X ≈ B that is appropriate when there is error in the matrix B. In this paper, by means of complex representation of a quaternion matrix, we introduce a concept of norm of quaternion...

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Bibliographic Details
Published in:Computer physics communications Vol. 176; no. 7; pp. 481 - 485
Main Authors: Jiang, Tongsong, Chen, Li
Format: Journal Article
Language:English
Published: Elsevier B.V 01.04.2007
Subjects:
Algorithm
Least squares
Quaternion matrix
Quaternionic quantum theory
Quaternionic quantum theory
Quaternion matrix
03.65.Fd
Least squares
Algorithm
02.10.Yn
04.25.Nx
ISSN:0010-4655, 1879-2944
Online Access:Get full text
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Summary:Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations A X ≈ B that is appropriate when there is error in the matrix B. In this paper, by means of complex representation of a quaternion matrix, we introduce a concept of norm of quaternion matrices, discuss singular values and generalized inverses of a quaternion matrix, study the QLS problem and derive two algebraic methods for finding solutions of the QLS problem in quaternionic quantum theory.
ISSN:0010-4655
1879-2944
DOI:10.1016/j.cpc.2006.12.005